x^2+8x-500=0

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Solution for x^2+8x-500=0 equation:


Simplifying
x2 + 8x + -500 = 0

Reorder the terms:
-500 + 8x + x2 = 0

Solving
-500 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 8x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + 8x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 8x + x2 = 0 + 500
8x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
8x + x2 = 500

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 500 + 16

Reorder the terms:
16 + 8x + x2 = 500 + 16

Combine like terms: 500 + 16 = 516
16 + 8x + x2 = 516

Factor a perfect square on the left side:
(x + 4)(x + 4) = 516

Calculate the square root of the right side: 22.715633383

Break this problem into two subproblems by setting 
(x + 4) equal to 22.715633383 and -22.715633383.

Subproblem 1

x + 4 = 22.715633383 Simplifying x + 4 = 22.715633383 Reorder the terms: 4 + x = 22.715633383 Solving 4 + x = 22.715633383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 22.715633383 + -4 Combine like terms: 4 + -4 = 0 0 + x = 22.715633383 + -4 x = 22.715633383 + -4 Combine like terms: 22.715633383 + -4 = 18.715633383 x = 18.715633383 Simplifying x = 18.715633383

Subproblem 2

x + 4 = -22.715633383 Simplifying x + 4 = -22.715633383 Reorder the terms: 4 + x = -22.715633383 Solving 4 + x = -22.715633383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -22.715633383 + -4 Combine like terms: 4 + -4 = 0 0 + x = -22.715633383 + -4 x = -22.715633383 + -4 Combine like terms: -22.715633383 + -4 = -26.715633383 x = -26.715633383 Simplifying x = -26.715633383

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.715633383, -26.715633383}

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