x*x+x*x-10x+25=18*18

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Solution for x*x+x*x-10x+25=18*18 equation:


Simplifying
x * x + x * x + -10x + 25 = 18 * 18

Multiply x * x
x2 + x * x + -10x + 25 = 18 * 18

Multiply x * x
x2 + x2 + -10x + 25 = 18 * 18

Reorder the terms:
25 + -10x + x2 + x2 = 18 * 18

Combine like terms: x2 + x2 = 2x2
25 + -10x + 2x2 = 18 * 18

Multiply 18 * 18
25 + -10x + 2x2 = 324

Solving
25 + -10x + 2x2 = 324

Solving for variable 'x'.

Reorder the terms:
25 + -324 + -10x + 2x2 = 324 + -324

Combine like terms: 25 + -324 = -299
-299 + -10x + 2x2 = 324 + -324

Combine like terms: 324 + -324 = 0
-299 + -10x + 2x2 = 0

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

Divide each side by '2'.
-149.5 + -5x + x2 = 0

Move the constant term to the right:

Add '149.5' to each side of the equation.
-149.5 + -5x + 149.5 + x2 = 0 + 149.5

Reorder the terms:
-149.5 + 149.5 + -5x + x2 = 0 + 149.5

Combine like terms: -149.5 + 149.5 = 0.0
0.0 + -5x + x2 = 0 + 149.5
-5x + x2 = 0 + 149.5

Combine like terms: 0 + 149.5 = 149.5
-5x + x2 = 149.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 149.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 149.5 + 6.25

Combine like terms: 149.5 + 6.25 = 155.75
6.25 + -5x + x2 = 155.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 155.75

Calculate the square root of the right side: 12.479983974

Break this problem into two subproblems by setting 
(x + -2.5) equal to 12.479983974 and -12.479983974.

Subproblem 1

x + -2.5 = 12.479983974 Simplifying x + -2.5 = 12.479983974 Reorder the terms: -2.5 + x = 12.479983974 Solving -2.5 + x = 12.479983974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 12.479983974 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 12.479983974 + 2.5 x = 12.479983974 + 2.5 Combine like terms: 12.479983974 + 2.5 = 14.979983974 x = 14.979983974 Simplifying x = 14.979983974

Subproblem 2

x + -2.5 = -12.479983974 Simplifying x + -2.5 = -12.479983974 Reorder the terms: -2.5 + x = -12.479983974 Solving -2.5 + x = -12.479983974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -12.479983974 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -12.479983974 + 2.5 x = -12.479983974 + 2.5 Combine like terms: -12.479983974 + 2.5 = -9.979983974 x = -9.979983974 Simplifying x = -9.979983974

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.979983974, -9.979983974}

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