x^2+8x+8=25

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


Simplifying
x2 + 8x + 8 = 25

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

Solving
8 + 8x + x2 = 25

Solving for variable 'x'.

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

Combine like terms: 8 + -25 = -17
-17 + 8x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-17 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 8x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 8x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 8x + x2 = 0 + 17
8x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
8x + x2 = 17

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 = 17 + 16

Reorder the terms:
16 + 8x + x2 = 17 + 16

Combine like terms: 17 + 16 = 33
16 + 8x + x2 = 33

Factor a perfect square on the left side:
(x + 4)(x + 4) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + 4) equal to 5.744562647 and -5.744562647.

Subproblem 1

x + 4 = 5.744562647 Simplifying x + 4 = 5.744562647 Reorder the terms: 4 + x = 5.744562647 Solving 4 + x = 5.744562647 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 = 5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.744562647 + -4 x = 5.744562647 + -4 Combine like terms: 5.744562647 + -4 = 1.744562647 x = 1.744562647 Simplifying x = 1.744562647

Subproblem 2

x + 4 = -5.744562647 Simplifying x + 4 = -5.744562647 Reorder the terms: 4 + x = -5.744562647 Solving 4 + x = -5.744562647 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 = -5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.744562647 + -4 x = -5.744562647 + -4 Combine like terms: -5.744562647 + -4 = -9.744562647 x = -9.744562647 Simplifying x = -9.744562647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.744562647, -9.744562647}

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