x^2+34x-60=0

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Solution for x^2+34x-60=0 equation:


Simplifying
x2 + 34x + -60 = 0

Reorder the terms:
-60 + 34x + x2 = 0

Solving
-60 + 34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 34x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 34x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 34x + x2 = 0 + 60
34x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
34x + x2 = 60

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 = 60 + 289

Reorder the terms:
289 + 34x + x2 = 60 + 289

Combine like terms: 60 + 289 = 349
289 + 34x + x2 = 349

Factor a perfect square on the left side:
(x + 17)(x + 17) = 349

Calculate the square root of the right side: 18.681541692

Break this problem into two subproblems by setting 
(x + 17) equal to 18.681541692 and -18.681541692.

Subproblem 1

x + 17 = 18.681541692 Simplifying x + 17 = 18.681541692 Reorder the terms: 17 + x = 18.681541692 Solving 17 + x = 18.681541692 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 = 18.681541692 + -17 Combine like terms: 17 + -17 = 0 0 + x = 18.681541692 + -17 x = 18.681541692 + -17 Combine like terms: 18.681541692 + -17 = 1.681541692 x = 1.681541692 Simplifying x = 1.681541692

Subproblem 2

x + 17 = -18.681541692 Simplifying x + 17 = -18.681541692 Reorder the terms: 17 + x = -18.681541692 Solving 17 + x = -18.681541692 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 = -18.681541692 + -17 Combine like terms: 17 + -17 = 0 0 + x = -18.681541692 + -17 x = -18.681541692 + -17 Combine like terms: -18.681541692 + -17 = -35.681541692 x = -35.681541692 Simplifying x = -35.681541692

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.681541692, -35.681541692}

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