(x+14)(x+14)+(x+17)(x+17)=(8x+9)(8x+9)

Solution for (x+14)(x+14)+(x+17)(x+17)=(8x+9)(8x+9) equation:

Simplifying
(x + 14)(x + 14) + (x + 17)(x + 17) = (8x + 9)(8x + 9)

Reorder the terms:
(14 + x)(x + 14) + (x + 17)(x + 17) = (8x + 9)(8x + 9)

Reorder the terms:
(14 + x)(14 + x) + (x + 17)(x + 17) = (8x + 9)(8x + 9)

Multiply (14 + x) * (14 + x)
(14(14 + x) + x(14 + x)) + (x + 17)(x + 17) = (8x + 9)(8x + 9)
((14 * 14 + x * 14) + x(14 + x)) + (x + 17)(x + 17) = (8x + 9)(8x + 9)
((196 + 14x) + x(14 + x)) + (x + 17)(x + 17) = (8x + 9)(8x + 9)
(196 + 14x + (14 * x + x * x)) + (x + 17)(x + 17) = (8x + 9)(8x + 9)
(196 + 14x + (14x + x2)) + (x + 17)(x + 17) = (8x + 9)(8x + 9)

Combine like terms: 14x + 14x = 28x
(196 + 28x + x2) + (x + 17)(x + 17) = (8x + 9)(8x + 9)

Reorder the terms:
196 + 28x + x2 + (17 + x)(x + 17) = (8x + 9)(8x + 9)

Reorder the terms:
196 + 28x + x2 + (17 + x)(17 + x) = (8x + 9)(8x + 9)

Multiply (17 + x) * (17 + x)
196 + 28x + x2 + (17(17 + x) + x(17 + x)) = (8x + 9)(8x + 9)
196 + 28x + x2 + ((17 * 17 + x * 17) + x(17 + x)) = (8x + 9)(8x + 9)
196 + 28x + x2 + ((289 + 17x) + x(17 + x)) = (8x + 9)(8x + 9)
196 + 28x + x2 + (289 + 17x + (17 * x + x * x)) = (8x + 9)(8x + 9)
196 + 28x + x2 + (289 + 17x + (17x + x2)) = (8x + 9)(8x + 9)

Combine like terms: 17x + 17x = 34x
196 + 28x + x2 + (289 + 34x + x2) = (8x + 9)(8x + 9)

Reorder the terms:
196 + 289 + 28x + 34x + x2 + x2 = (8x + 9)(8x + 9)

Combine like terms: 196 + 289 = 485
485 + 28x + 34x + x2 + x2 = (8x + 9)(8x + 9)

Combine like terms: 28x + 34x = 62x
485 + 62x + x2 + x2 = (8x + 9)(8x + 9)

Combine like terms: x2 + x2 = 2x2
485 + 62x + 2x2 = (8x + 9)(8x + 9)

Reorder the terms:
485 + 62x + 2x2 = (9 + 8x)(8x + 9)

Reorder the terms:
485 + 62x + 2x2 = (9 + 8x)(9 + 8x)

Multiply (9 + 8x) * (9 + 8x)
485 + 62x + 2x2 = (9(9 + 8x) + 8x * (9 + 8x))
485 + 62x + 2x2 = ((9 * 9 + 8x * 9) + 8x * (9 + 8x))
485 + 62x + 2x2 = ((81 + 72x) + 8x * (9 + 8x))
485 + 62x + 2x2 = (81 + 72x + (9 * 8x + 8x * 8x))
485 + 62x + 2x2 = (81 + 72x + (72x + 64x2))

Combine like terms: 72x + 72x = 144x
485 + 62x + 2x2 = (81 + 144x + 64x2)

Solving
485 + 62x + 2x2 = 81 + 144x + 64x2

Solving for variable 'x'.

Reorder the terms:
485 + -81 + 62x + -144x + 2x2 + -64x2 = 81 + 144x + 64x2 + -81 + -144x + -64x2

Combine like terms: 485 + -81 = 404
404 + 62x + -144x + 2x2 + -64x2 = 81 + 144x + 64x2 + -81 + -144x + -64x2

Combine like terms: 62x + -144x = -82x
404 + -82x + 2x2 + -64x2 = 81 + 144x + 64x2 + -81 + -144x + -64x2

Combine like terms: 2x2 + -64x2 = -62x2
404 + -82x + -62x2 = 81 + 144x + 64x2 + -81 + -144x + -64x2

Reorder the terms:
404 + -82x + -62x2 = 81 + -81 + 144x + -144x + 64x2 + -64x2

Combine like terms: 81 + -81 = 0
404 + -82x + -62x2 = 0 + 144x + -144x + 64x2 + -64x2
404 + -82x + -62x2 = 144x + -144x + 64x2 + -64x2

Combine like terms: 144x + -144x = 0
404 + -82x + -62x2 = 0 + 64x2 + -64x2
404 + -82x + -62x2 = 64x2 + -64x2

Combine like terms: 64x2 + -64x2 = 0
404 + -82x + -62x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(202 + -41x + -31x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(202 + -41x + -31x2)' equal to zero and attempt to solve:

Simplifying
202 + -41x + -31x2 = 0

Solving
202 + -41x + -31x2 = 0

Begin completing the square.  Divide all terms by
-31 the coefficient of the squared term: 

Divide each side by '-31'.
-6.516129032 + 1.322580645x + x2 = 0

Move the constant term to the right:

Add '6.516129032' to each side of the equation.
-6.516129032 + 1.322580645x + 6.516129032 + x2 = 0 + 6.516129032

Reorder the terms:
-6.516129032 + 6.516129032 + 1.322580645x + x2 = 0 + 6.516129032

Combine like terms: -6.516129032 + 6.516129032 = 0.000000000
0.000000000 + 1.322580645x + x2 = 0 + 6.516129032
1.322580645x + x2 = 0 + 6.516129032

Combine like terms: 0 + 6.516129032 = 6.516129032
1.322580645x + x2 = 6.516129032

The x term is 1.322580645x.  Take half its coefficient (0.6612903225).
Square it (0.4373048906) and add it to both sides.

Add '0.4373048906' to each side of the equation.
1.322580645x + 0.4373048906 + x2 = 6.516129032 + 0.4373048906

Reorder the terms:
0.4373048906 + 1.322580645x + x2 = 6.516129032 + 0.4373048906

Combine like terms: 6.516129032 + 0.4373048906 = 6.9534339226
0.4373048906 + 1.322580645x + x2 = 6.9534339226

Factor a perfect square on the left side:
(x + 0.6612903225)(x + 0.6612903225) = 6.9534339226

Calculate the square root of the right side: 2.636936465

Break this problem into two subproblems by setting 
(x + 0.6612903225) equal to 2.636936465 and -2.636936465.

Subproblem 1
x + 0.6612903225 = 2.636936465

Simplifying
x + 0.6612903225 = 2.636936465

Reorder the terms:
0.6612903225 + x = 2.636936465

Solving
0.6612903225 + x = 2.636936465

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.6612903225' to each side of the equation.
0.6612903225 + -0.6612903225 + x = 2.636936465 + -0.6612903225

Combine like terms: 0.6612903225 + -0.6612903225 = 0.0000000000
0.0000000000 + x = 2.636936465 + -0.6612903225
x = 2.636936465 + -0.6612903225

Combine like terms: 2.636936465 + -0.6612903225 = 1.9756461425
x = 1.9756461425

Simplifying
x = 1.9756461425

Subproblem 2
x + 0.6612903225 = -2.636936465

Simplifying
x + 0.6612903225 = -2.636936465

Reorder the terms:
0.6612903225 + x = -2.636936465

Solving
0.6612903225 + x = -2.636936465

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.6612903225' to each side of the equation.
0.6612903225 + -0.6612903225 + x = -2.636936465 + -0.6612903225

Combine like terms: 0.6612903225 + -0.6612903225 = 0.0000000000
0.0000000000 + x = -2.636936465 + -0.6612903225
x = -2.636936465 + -0.6612903225

Combine like terms: -2.636936465 + -0.6612903225 = -3.2982267875
x = -3.2982267875

Simplifying
x = -3.2982267875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.9756461425, -3.2982267875}
Solution
x = {1.9756461425, -3.2982267875}