x^2+16x+64=11

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Solution for x^2+16x+64=11 equation:


Simplifying
x2 + 16x + 64 = 11

Reorder the terms:
64 + 16x + x2 = 11

Solving
64 + 16x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
64 + -11 + 16x + x2 = 11 + -11

Combine like terms: 64 + -11 = 53
53 + 16x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
53 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-53' to each side of the equation.
53 + 16x + -53 + x2 = 0 + -53

Reorder the terms:
53 + -53 + 16x + x2 = 0 + -53

Combine like terms: 53 + -53 = 0
0 + 16x + x2 = 0 + -53
16x + x2 = 0 + -53

Combine like terms: 0 + -53 = -53
16x + x2 = -53

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 = -53 + 64

Reorder the terms:
64 + 16x + x2 = -53 + 64

Combine like terms: -53 + 64 = 11
64 + 16x + x2 = 11

Factor a perfect square on the left side:
(x + 8)(x + 8) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 8) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + 8 = 3.31662479 Simplifying x + 8 = 3.31662479 Reorder the terms: 8 + x = 3.31662479 Solving 8 + x = 3.31662479 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 = 3.31662479 + -8 Combine like terms: 8 + -8 = 0 0 + x = 3.31662479 + -8 x = 3.31662479 + -8 Combine like terms: 3.31662479 + -8 = -4.68337521 x = -4.68337521 Simplifying x = -4.68337521

Subproblem 2

x + 8 = -3.31662479 Simplifying x + 8 = -3.31662479 Reorder the terms: 8 + x = -3.31662479 Solving 8 + x = -3.31662479 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 = -3.31662479 + -8 Combine like terms: 8 + -8 = 0 0 + x = -3.31662479 + -8 x = -3.31662479 + -8 Combine like terms: -3.31662479 + -8 = -11.31662479 x = -11.31662479 Simplifying x = -11.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.68337521, -11.31662479}

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