x^2+34x+81=0

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Solution for x^2+34x+81=0 equation:


Simplifying
x2 + 34x + 81 = 0

Reorder the terms:
81 + 34x + x2 = 0

Solving
81 + 34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + 34x + -81 + x2 = 0 + -81

Reorder the terms:
81 + -81 + 34x + x2 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + 34x + x2 = 0 + -81
34x + x2 = 0 + -81

Combine like terms: 0 + -81 = -81
34x + x2 = -81

The x term is 34x.  Take half its coefficient (17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
34x + 289 + x2 = -81 + 289

Reorder the terms:
289 + 34x + x2 = -81 + 289

Combine like terms: -81 + 289 = 208
289 + 34x + x2 = 208

Factor a perfect square on the left side:
(x + 17)(x + 17) = 208

Calculate the square root of the right side: 14.422205102

Break this problem into two subproblems by setting 
(x + 17) equal to 14.422205102 and -14.422205102.

Subproblem 1

x + 17 = 14.422205102 Simplifying x + 17 = 14.422205102 Reorder the terms: 17 + x = 14.422205102 Solving 17 + x = 14.422205102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 14.422205102 + -17 Combine like terms: 17 + -17 = 0 0 + x = 14.422205102 + -17 x = 14.422205102 + -17 Combine like terms: 14.422205102 + -17 = -2.577794898 x = -2.577794898 Simplifying x = -2.577794898

Subproblem 2

x + 17 = -14.422205102 Simplifying x + 17 = -14.422205102 Reorder the terms: 17 + x = -14.422205102 Solving 17 + x = -14.422205102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -14.422205102 + -17 Combine like terms: 17 + -17 = 0 0 + x = -14.422205102 + -17 x = -14.422205102 + -17 Combine like terms: -14.422205102 + -17 = -31.422205102 x = -31.422205102 Simplifying x = -31.422205102

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.577794898, -31.422205102}

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