x^2+16x=-7

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Solution for x^2+16x=-7 equation:


Simplifying
x2 + 16x = -7

Reorder the terms:
16x + x2 = -7

Solving
16x + x2 = -7

Solving for variable 'x'.

Reorder the terms:
7 + 16x + x2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 16x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 16x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 16x + x2 = 0 + -7
16x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
16x + x2 = -7

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -7 + 64

Reorder the terms:
64 + 16x + x2 = -7 + 64

Combine like terms: -7 + 64 = 57
64 + 16x + x2 = 57

Factor a perfect square on the left side:
(x + 8)(x + 8) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + 8) equal to 7.549834435 and -7.549834435.

Subproblem 1

x + 8 = 7.549834435 Simplifying x + 8 = 7.549834435 Reorder the terms: 8 + x = 7.549834435 Solving 8 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 7.549834435 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.549834435 + -8 x = 7.549834435 + -8 Combine like terms: 7.549834435 + -8 = -0.450165565 x = -0.450165565 Simplifying x = -0.450165565

Subproblem 2

x + 8 = -7.549834435 Simplifying x + 8 = -7.549834435 Reorder the terms: 8 + x = -7.549834435 Solving 8 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -7.549834435 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.549834435 + -8 x = -7.549834435 + -8 Combine like terms: -7.549834435 + -8 = -15.549834435 x = -15.549834435 Simplifying x = -15.549834435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.450165565, -15.549834435}

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