x^2+16x=61

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Solution for x^2+16x=61 equation:


Simplifying
x2 + 16x = 61

Reorder the terms:
16x + x2 = 61

Solving
16x + x2 = 61

Solving for variable 'x'.

Reorder the terms:
-61 + 16x + x2 = 61 + -61

Combine like terms: 61 + -61 = 0
-61 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + 16x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + 16x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 16x + x2 = 0 + 61
16x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
16x + x2 = 61

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 = 61 + 64

Reorder the terms:
64 + 16x + x2 = 61 + 64

Combine like terms: 61 + 64 = 125
64 + 16x + x2 = 125

Factor a perfect square on the left side:
(x + 8)(x + 8) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + 8) equal to 11.180339887 and -11.180339887.

Subproblem 1

x + 8 = 11.180339887 Simplifying x + 8 = 11.180339887 Reorder the terms: 8 + x = 11.180339887 Solving 8 + x = 11.180339887 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 = 11.180339887 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.180339887 + -8 x = 11.180339887 + -8 Combine like terms: 11.180339887 + -8 = 3.180339887 x = 3.180339887 Simplifying x = 3.180339887

Subproblem 2

x + 8 = -11.180339887 Simplifying x + 8 = -11.180339887 Reorder the terms: 8 + x = -11.180339887 Solving 8 + x = -11.180339887 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 = -11.180339887 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.180339887 + -8 x = -11.180339887 + -8 Combine like terms: -11.180339887 + -8 = -19.180339887 x = -19.180339887 Simplifying x = -19.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.180339887, -19.180339887}

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