x^2+16x+64=41

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Solution for x^2+16x+64=41 equation:


Simplifying
x2 + 16x + 64 = 41

Reorder the terms:
64 + 16x + x2 = 41

Solving
64 + 16x + x2 = 41

Solving for variable 'x'.

Reorder the terms:
64 + -41 + 16x + x2 = 41 + -41

Combine like terms: 64 + -41 = 23
23 + 16x + x2 = 41 + -41

Combine like terms: 41 + -41 = 0
23 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 16x + -23 + x2 = 0 + -23

Reorder the terms:
23 + -23 + 16x + x2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 16x + x2 = 0 + -23
16x + x2 = 0 + -23

Combine like terms: 0 + -23 = -23
16x + x2 = -23

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 = -23 + 64

Reorder the terms:
64 + 16x + x2 = -23 + 64

Combine like terms: -23 + 64 = 41
64 + 16x + x2 = 41

Factor a perfect square on the left side:
(x + 8)(x + 8) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 8) equal to 6.403124237 and -6.403124237.

Subproblem 1

x + 8 = 6.403124237 Simplifying x + 8 = 6.403124237 Reorder the terms: 8 + x = 6.403124237 Solving 8 + x = 6.403124237 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 = 6.403124237 + -8 Combine like terms: 8 + -8 = 0 0 + x = 6.403124237 + -8 x = 6.403124237 + -8 Combine like terms: 6.403124237 + -8 = -1.596875763 x = -1.596875763 Simplifying x = -1.596875763

Subproblem 2

x + 8 = -6.403124237 Simplifying x + 8 = -6.403124237 Reorder the terms: 8 + x = -6.403124237 Solving 8 + x = -6.403124237 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 = -6.403124237 + -8 Combine like terms: 8 + -8 = 0 0 + x = -6.403124237 + -8 x = -6.403124237 + -8 Combine like terms: -6.403124237 + -8 = -14.403124237 x = -14.403124237 Simplifying x = -14.403124237

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.596875763, -14.403124237}

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