x^2=100+10x

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Solution for x^2=100+10x equation:


Simplifying
x2 = 100 + 10x

Solving
x2 = 100 + 10x

Solving for variable 'x'.

Reorder the terms:
-100 + -10x + x2 = 100 + 10x + -100 + -10x

Reorder the terms:
-100 + -10x + x2 = 100 + -100 + 10x + -10x

Combine like terms: 100 + -100 = 0
-100 + -10x + x2 = 0 + 10x + -10x
-100 + -10x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-100 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -10x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + -10x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -10x + x2 = 0 + 100
-10x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-10x + x2 = 100

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 100 + 25

Reorder the terms:
25 + -10x + x2 = 100 + 25

Combine like terms: 100 + 25 = 125
25 + -10x + x2 = 125

Factor a perfect square on the left side:
(x + -5)(x + -5) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + -5) equal to 11.180339887 and -11.180339887.

Subproblem 1

x + -5 = 11.180339887 Simplifying x + -5 = 11.180339887 Reorder the terms: -5 + x = 11.180339887 Solving -5 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 11.180339887 + 5 Combine like terms: -5 + 5 = 0 0 + x = 11.180339887 + 5 x = 11.180339887 + 5 Combine like terms: 11.180339887 + 5 = 16.180339887 x = 16.180339887 Simplifying x = 16.180339887

Subproblem 2

x + -5 = -11.180339887 Simplifying x + -5 = -11.180339887 Reorder the terms: -5 + x = -11.180339887 Solving -5 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -11.180339887 + 5 Combine like terms: -5 + 5 = 0 0 + x = -11.180339887 + 5 x = -11.180339887 + 5 Combine like terms: -11.180339887 + 5 = -6.180339887 x = -6.180339887 Simplifying x = -6.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.180339887, -6.180339887}

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