-x^2-8x+5=0

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Solution for -x^2-8x+5=0 equation:


Simplifying
-1x2 + -8x + 5 = 0

Reorder the terms:
5 + -8x + -1x2 = 0

Solving
5 + -8x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-5 + 8x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 8x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 8x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 8x + x2 = 0 + 5
8x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
8x + x2 = 5

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 = 5 + 16

Reorder the terms:
16 + 8x + x2 = 5 + 16

Combine like terms: 5 + 16 = 21
16 + 8x + x2 = 21

Factor a perfect square on the left side:
(x + 4)(x + 4) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + 4) equal to 4.582575695 and -4.582575695.

Subproblem 1

x + 4 = 4.582575695 Simplifying x + 4 = 4.582575695 Reorder the terms: 4 + x = 4.582575695 Solving 4 + x = 4.582575695 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 = 4.582575695 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.582575695 + -4 x = 4.582575695 + -4 Combine like terms: 4.582575695 + -4 = 0.582575695 x = 0.582575695 Simplifying x = 0.582575695

Subproblem 2

x + 4 = -4.582575695 Simplifying x + 4 = -4.582575695 Reorder the terms: 4 + x = -4.582575695 Solving 4 + x = -4.582575695 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 = -4.582575695 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.582575695 + -4 x = -4.582575695 + -4 Combine like terms: -4.582575695 + -4 = -8.582575695 x = -8.582575695 Simplifying x = -8.582575695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.582575695, -8.582575695}

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