x^2+8x+5=2

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


Simplifying
x2 + 8x + 5 = 2

Reorder the terms:
5 + 8x + x2 = 2

Solving
5 + 8x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
5 + -2 + 8x + x2 = 2 + -2

Combine like terms: 5 + -2 = 3
3 + 8x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
3 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 8x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 8x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8x + x2 = 0 + -3
8x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
8x + x2 = -3

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 = -3 + 16

Reorder the terms:
16 + 8x + x2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + 8x + x2 = 13

Factor a perfect square on the left side:
(x + 4)(x + 4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 4) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + 4 = 3.605551275 Simplifying x + 4 = 3.605551275 Reorder the terms: 4 + x = 3.605551275 Solving 4 + x = 3.605551275 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 = 3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.605551275 + -4 x = 3.605551275 + -4 Combine like terms: 3.605551275 + -4 = -0.394448725 x = -0.394448725 Simplifying x = -0.394448725

Subproblem 2

x + 4 = -3.605551275 Simplifying x + 4 = -3.605551275 Reorder the terms: 4 + x = -3.605551275 Solving 4 + x = -3.605551275 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 = -3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.605551275 + -4 x = -3.605551275 + -4 Combine like terms: -3.605551275 + -4 = -7.605551275 x = -7.605551275 Simplifying x = -7.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.394448725, -7.605551275}

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