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 = 370
289 + 34x + x2 = 370

Factor a perfect square on the left side:
(x + 17)(x + 17) = 370

Calculate the square root of the right side: 19.235384062

Break this problem into two subproblems by setting 
(x + 17) equal to 19.235384062 and -19.235384062.

Subproblem 1

x + 17 = 19.235384062 Simplifying x + 17 = 19.235384062 Reorder the terms: 17 + x = 19.235384062 Solving 17 + x = 19.235384062 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 = 19.235384062 + -17 Combine like terms: 17 + -17 = 0 0 + x = 19.235384062 + -17 x = 19.235384062 + -17 Combine like terms: 19.235384062 + -17 = 2.235384062 x = 2.235384062 Simplifying x = 2.235384062

Subproblem 2

x + 17 = -19.235384062 Simplifying x + 17 = -19.235384062 Reorder the terms: 17 + x = -19.235384062 Solving 17 + x = -19.235384062 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 = -19.235384062 + -17 Combine like terms: 17 + -17 = 0 0 + x = -19.235384062 + -17 x = -19.235384062 + -17 Combine like terms: -19.235384062 + -17 = -36.235384062 x = -36.235384062 Simplifying x = -36.235384062

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.235384062, -36.235384062}

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