x^2+31x-60=0

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Solution for x^2+31x-60=0 equation:


Simplifying
x2 + 31x + -60 = 0

Reorder the terms:
-60 + 31x + x2 = 0

Solving
-60 + 31x + 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 + 31x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 31x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 31x + x2 = 0 + 60
31x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
31x + x2 = 60

The x term is 31x.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31x + 240.25 + x2 = 60 + 240.25

Reorder the terms:
240.25 + 31x + x2 = 60 + 240.25

Combine like terms: 60 + 240.25 = 300.25
240.25 + 31x + x2 = 300.25

Factor a perfect square on the left side:
(x + 15.5)(x + 15.5) = 300.25

Calculate the square root of the right side: 17.327723451

Break this problem into two subproblems by setting 
(x + 15.5) equal to 17.327723451 and -17.327723451.

Subproblem 1

x + 15.5 = 17.327723451 Simplifying x + 15.5 = 17.327723451 Reorder the terms: 15.5 + x = 17.327723451 Solving 15.5 + x = 17.327723451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 17.327723451 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 17.327723451 + -15.5 x = 17.327723451 + -15.5 Combine like terms: 17.327723451 + -15.5 = 1.827723451 x = 1.827723451 Simplifying x = 1.827723451

Subproblem 2

x + 15.5 = -17.327723451 Simplifying x + 15.5 = -17.327723451 Reorder the terms: 15.5 + x = -17.327723451 Solving 15.5 + x = -17.327723451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -17.327723451 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -17.327723451 + -15.5 x = -17.327723451 + -15.5 Combine like terms: -17.327723451 + -15.5 = -32.827723451 x = -32.827723451 Simplifying x = -32.827723451

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.827723451, -32.827723451}

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