5x^2-8x-60=0

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Solution for 5x^2-8x-60=0 equation:


Simplifying
5x2 + -8x + -60 = 0

Reorder the terms:
-60 + -8x + 5x2 = 0

Solving
-60 + -8x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-12 + -1.6x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -1.6x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -1.6x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1.6x + x2 = 0 + 12
-1.6x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-1.6x + x2 = 12

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 12 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 12 + 0.64

Combine like terms: 12 + 0.64 = 12.64
0.64 + -1.6x + x2 = 12.64

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 12.64

Calculate the square root of the right side: 3.555277767

Break this problem into two subproblems by setting 
(x + -0.8) equal to 3.555277767 and -3.555277767.

Subproblem 1

x + -0.8 = 3.555277767 Simplifying x + -0.8 = 3.555277767 Reorder the terms: -0.8 + x = 3.555277767 Solving -0.8 + x = 3.555277767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 3.555277767 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 3.555277767 + 0.8 x = 3.555277767 + 0.8 Combine like terms: 3.555277767 + 0.8 = 4.355277767 x = 4.355277767 Simplifying x = 4.355277767

Subproblem 2

x + -0.8 = -3.555277767 Simplifying x + -0.8 = -3.555277767 Reorder the terms: -0.8 + x = -3.555277767 Solving -0.8 + x = -3.555277767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -3.555277767 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -3.555277767 + 0.8 x = -3.555277767 + 0.8 Combine like terms: -3.555277767 + 0.8 = -2.755277767 x = -2.755277767 Simplifying x = -2.755277767

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.355277767, -2.755277767}

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