x^2+44+16x=180

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Solution for x^2+44+16x=180 equation:


Simplifying
x2 + 44 + 16x = 180

Reorder the terms:
44 + 16x + x2 = 180

Solving
44 + 16x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
44 + -180 + 16x + x2 = 180 + -180

Combine like terms: 44 + -180 = -136
-136 + 16x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-136 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '136' to each side of the equation.
-136 + 16x + 136 + x2 = 0 + 136

Reorder the terms:
-136 + 136 + 16x + x2 = 0 + 136

Combine like terms: -136 + 136 = 0
0 + 16x + x2 = 0 + 136
16x + x2 = 0 + 136

Combine like terms: 0 + 136 = 136
16x + x2 = 136

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 = 136 + 64

Reorder the terms:
64 + 16x + x2 = 136 + 64

Combine like terms: 136 + 64 = 200
64 + 16x + x2 = 200

Factor a perfect square on the left side:
(x + 8)(x + 8) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(x + 8) equal to 14.142135624 and -14.142135624.

Subproblem 1

x + 8 = 14.142135624 Simplifying x + 8 = 14.142135624 Reorder the terms: 8 + x = 14.142135624 Solving 8 + x = 14.142135624 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 = 14.142135624 + -8 Combine like terms: 8 + -8 = 0 0 + x = 14.142135624 + -8 x = 14.142135624 + -8 Combine like terms: 14.142135624 + -8 = 6.142135624 x = 6.142135624 Simplifying x = 6.142135624

Subproblem 2

x + 8 = -14.142135624 Simplifying x + 8 = -14.142135624 Reorder the terms: 8 + x = -14.142135624 Solving 8 + x = -14.142135624 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 = -14.142135624 + -8 Combine like terms: 8 + -8 = 0 0 + x = -14.142135624 + -8 x = -14.142135624 + -8 Combine like terms: -14.142135624 + -8 = -22.142135624 x = -22.142135624 Simplifying x = -22.142135624

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.142135624, -22.142135624}

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