x-4=x^2-100

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Solution for x-4=x^2-100 equation:


Simplifying
x + -4 = x2 + -100

Reorder the terms:
-4 + x = x2 + -100

Reorder the terms:
-4 + x = -100 + x2

Solving
-4 + x = -100 + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 100 + x + -1x2 = -100 + x2 + 100 + -1x2

Combine like terms: -4 + 100 = 96
96 + x + -1x2 = -100 + x2 + 100 + -1x2

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

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-96 + -1x + x2 = 0

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + -1x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + -1x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + -1x + x2 = 0 + 96
-1x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
-1x + x2 = 96

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.
-1x + 0.25 + x2 = 96 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 96 + 0.25

Combine like terms: 96 + 0.25 = 96.25
0.25 + -1x + x2 = 96.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.810708435 and -9.810708435.

Subproblem 1

x + 0.5 = 9.810708435 Simplifying x + 0.5 = 9.810708435 Reorder the terms: 0.5 + x = 9.810708435 Solving 0.5 + x = 9.810708435 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 = 9.810708435 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.810708435 + -0.5 x = 9.810708435 + -0.5 Combine like terms: 9.810708435 + -0.5 = 9.310708435 x = 9.310708435 Simplifying x = 9.310708435

Subproblem 2

x + 0.5 = -9.810708435 Simplifying x + 0.5 = -9.810708435 Reorder the terms: 0.5 + x = -9.810708435 Solving 0.5 + x = -9.810708435 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 = -9.810708435 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.810708435 + -0.5 x = -9.810708435 + -0.5 Combine like terms: -9.810708435 + -0.5 = -10.310708435 x = -10.310708435 Simplifying x = -10.310708435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.310708435, -10.310708435}

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