-8x-x^2=-25

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Solution for -8x-x^2=-25 equation:


Simplifying
-8x + -1x2 = -25

Solving
-8x + -1x2 = -25

Solving for variable 'x'.

Reorder the terms:
25 + -8x + -1x2 = -25 + 25

Combine like terms: -25 + 25 = 0
25 + -8x + -1x2 = 0

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

Divide each side by '-1'.
-25 + 8x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 8x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 8x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 8x + x2 = 0 + 25
8x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
8x + x2 = 25

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 = 25 + 16

Reorder the terms:
16 + 8x + x2 = 25 + 16

Combine like terms: 25 + 16 = 41
16 + 8x + x2 = 41

Factor a perfect square on the left side:
(x + 4)(x + 4) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 4) equal to 6.403124237 and -6.403124237.

Subproblem 1

x + 4 = 6.403124237 Simplifying x + 4 = 6.403124237 Reorder the terms: 4 + x = 6.403124237 Solving 4 + x = 6.403124237 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 = 6.403124237 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.403124237 + -4 x = 6.403124237 + -4 Combine like terms: 6.403124237 + -4 = 2.403124237 x = 2.403124237 Simplifying x = 2.403124237

Subproblem 2

x + 4 = -6.403124237 Simplifying x + 4 = -6.403124237 Reorder the terms: 4 + x = -6.403124237 Solving 4 + x = -6.403124237 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 = -6.403124237 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.403124237 + -4 x = -6.403124237 + -4 Combine like terms: -6.403124237 + -4 = -10.403124237 x = -10.403124237 Simplifying x = -10.403124237

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.403124237, -10.403124237}

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