(4x+10)4x=90

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Solution for (4x+10)4x=90 equation: 


Simplifying
(4x + 10) * 4x = 90

Reorder the terms:
(10 + 4x) * 4x = 90

Reorder the terms for easier multiplication:
4x(10 + 4x) = 90
(10 * 4x + 4x * 4x) = 90
(40x + 16x2) = 90

Solving
40x + 16x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 40x + 16x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 40x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 20x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 20x + 8x2)' equal to zero and attempt to solve:

Simplifying
-45 + 20x + 8x2 = 0

Solving
-45 + 20x + 8x2 = 0

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

Divide each side by '8'.
-5.625 + 2.5x + x2 = 0

Move the constant term to the right:

Add '5.625' to each side of the equation.
-5.625 + 2.5x + 5.625 + x2 = 0 + 5.625

Reorder the terms:
-5.625 + 5.625 + 2.5x + x2 = 0 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + 2.5x + x2 = 0 + 5.625
2.5x + x2 = 0 + 5.625

Combine like terms: 0 + 5.625 = 5.625
2.5x + x2 = 5.625

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 5.625 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 5.625 + 1.5625

Combine like terms: 5.625 + 1.5625 = 7.1875
1.5625 + 2.5x + x2 = 7.1875

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 7.1875

Calculate the square root of the right side: 2.680951324

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.680951324 and -2.680951324.


Subproblem 1
x + 1.25 = 2.680951324

Simplifying
x + 1.25 = 2.680951324

Reorder the terms:
1.25 + x = 2.680951324

Solving
1.25 + x = 2.680951324

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 2.680951324 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.680951324 + -1.25
x = 2.680951324 + -1.25

Combine like terms: 2.680951324 + -1.25 = 1.430951324
x = 1.430951324

Simplifying
x = 1.430951324


Subproblem 2
x + 1.25 = -2.680951324

Simplifying
x + 1.25 = -2.680951324

Reorder the terms:
1.25 + x = -2.680951324

Solving
1.25 + x = -2.680951324

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -2.680951324 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.680951324 + -1.25
x = -2.680951324 + -1.25

Combine like terms: -2.680951324 + -1.25 = -3.930951324
x = -3.930951324

Simplifying
x = -3.930951324


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.430951324, -3.930951324}
Solution
x = {1.430951324, -3.930951324}

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