x^2=100-x

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Solution for x^2=100-x equation:


Simplifying
x2 = 100 + -1x

Solving
x2 = 100 + -1x

Solving for variable 'x'.

Reorder the terms:
-100 + x + x2 = 100 + -1x + -100 + x

Reorder the terms:
-100 + x + x2 = 100 + -100 + -1x + x

Combine like terms: 100 + -100 = 0
-100 + x + x2 = 0 + -1x + x
-100 + x + x2 = -1x + x

Combine like terms: -1x + x = 0
-100 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 100 + 0.25

Reorder the terms:
0.25 + x + x2 = 100 + 0.25

Combine like terms: 100 + 0.25 = 100.25
0.25 + x + x2 = 100.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(x + 0.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

x + 0.5 = 10.012492197 Simplifying x + 0.5 = 10.012492197 Reorder the terms: 0.5 + x = 10.012492197 Solving 0.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.012492197 + -0.5 x = 10.012492197 + -0.5 Combine like terms: 10.012492197 + -0.5 = 9.512492197 x = 9.512492197 Simplifying x = 9.512492197

Subproblem 2

x + 0.5 = -10.012492197 Simplifying x + 0.5 = -10.012492197 Reorder the terms: 0.5 + x = -10.012492197 Solving 0.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.012492197 + -0.5 x = -10.012492197 + -0.5 Combine like terms: -10.012492197 + -0.5 = -10.512492197 x = -10.512492197 Simplifying x = -10.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.512492197, -10.512492197}

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