x^2+16x-34=-8x-1

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Solution for x^2+16x-34=-8x-1 equation:


Simplifying
x2 + 16x + -34 = -8x + -1

Reorder the terms:
-34 + 16x + x2 = -8x + -1

Reorder the terms:
-34 + 16x + x2 = -1 + -8x

Solving
-34 + 16x + x2 = -1 + -8x

Solving for variable 'x'.

Reorder the terms:
-34 + 1 + 16x + 8x + x2 = -1 + -8x + 1 + 8x

Combine like terms: -34 + 1 = -33
-33 + 16x + 8x + x2 = -1 + -8x + 1 + 8x

Combine like terms: 16x + 8x = 24x
-33 + 24x + x2 = -1 + -8x + 1 + 8x

Reorder the terms:
-33 + 24x + x2 = -1 + 1 + -8x + 8x

Combine like terms: -1 + 1 = 0
-33 + 24x + x2 = 0 + -8x + 8x
-33 + 24x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-33 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 24x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + 24x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 24x + x2 = 0 + 33
24x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
24x + x2 = 33

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 33 + 144

Reorder the terms:
144 + 24x + x2 = 33 + 144

Combine like terms: 33 + 144 = 177
144 + 24x + x2 = 177

Factor a perfect square on the left side:
(x + 12)(x + 12) = 177

Calculate the square root of the right side: 13.304134696

Break this problem into two subproblems by setting 
(x + 12) equal to 13.304134696 and -13.304134696.

Subproblem 1

x + 12 = 13.304134696 Simplifying x + 12 = 13.304134696 Reorder the terms: 12 + x = 13.304134696 Solving 12 + x = 13.304134696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 13.304134696 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.304134696 + -12 x = 13.304134696 + -12 Combine like terms: 13.304134696 + -12 = 1.304134696 x = 1.304134696 Simplifying x = 1.304134696

Subproblem 2

x + 12 = -13.304134696 Simplifying x + 12 = -13.304134696 Reorder the terms: 12 + x = -13.304134696 Solving 12 + x = -13.304134696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -13.304134696 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.304134696 + -12 x = -13.304134696 + -12 Combine like terms: -13.304134696 + -12 = -25.304134696 x = -25.304134696 Simplifying x = -25.304134696

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.304134696, -25.304134696}

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