x^2=x+99

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Solution for x^2=x+99 equation:


Simplifying
x2 = x + 99

Reorder the terms:
x2 = 99 + x

Solving
x2 = 99 + x

Solving for variable 'x'.

Reorder the terms:
-99 + -1x + x2 = 99 + x + -99 + -1x

Reorder the terms:
-99 + -1x + x2 = 99 + -99 + x + -1x

Combine like terms: 99 + -99 = 0
-99 + -1x + x2 = 0 + x + -1x
-99 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-99 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '99' to each side of the equation.
-99 + -1x + 99 + x2 = 0 + 99

Reorder the terms:
-99 + 99 + -1x + x2 = 0 + 99

Combine like terms: -99 + 99 = 0
0 + -1x + x2 = 0 + 99
-1x + x2 = 0 + 99

Combine like terms: 0 + 99 = 99
-1x + x2 = 99

The x term is -1x.  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.
-1x + 0.25 + x2 = 99 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 99 + 0.25

Combine like terms: 99 + 0.25 = 99.25
0.25 + -1x + x2 = 99.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 99.25

Calculate the square root of the right side: 9.962429423

Break this problem into two subproblems by setting 
(x + -0.5) equal to 9.962429423 and -9.962429423.

Subproblem 1

x + -0.5 = 9.962429423 Simplifying x + -0.5 = 9.962429423 Reorder the terms: -0.5 + x = 9.962429423 Solving -0.5 + x = 9.962429423 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 = 9.962429423 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.962429423 + 0.5 x = 9.962429423 + 0.5 Combine like terms: 9.962429423 + 0.5 = 10.462429423 x = 10.462429423 Simplifying x = 10.462429423

Subproblem 2

x + -0.5 = -9.962429423 Simplifying x + -0.5 = -9.962429423 Reorder the terms: -0.5 + x = -9.962429423 Solving -0.5 + x = -9.962429423 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 = -9.962429423 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.962429423 + 0.5 x = -9.962429423 + 0.5 Combine like terms: -9.962429423 + 0.5 = -9.462429423 x = -9.462429423 Simplifying x = -9.462429423

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.462429423, -9.462429423}

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