4x^2-60x-65=0

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Solution for 4x^2-60x-65=0 equation:


Simplifying
4x2 + -60x + -65 = 0

Reorder the terms:
-65 + -60x + 4x2 = 0

Solving
-65 + -60x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-16.25 + -15x + x2 = 0

Move the constant term to the right:

Add '16.25' to each side of the equation.
-16.25 + -15x + 16.25 + x2 = 0 + 16.25

Reorder the terms:
-16.25 + 16.25 + -15x + x2 = 0 + 16.25

Combine like terms: -16.25 + 16.25 = 0.00
0.00 + -15x + x2 = 0 + 16.25
-15x + x2 = 0 + 16.25

Combine like terms: 0 + 16.25 = 16.25
-15x + x2 = 16.25

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 16.25 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 16.25 + 56.25

Combine like terms: 16.25 + 56.25 = 72.5
56.25 + -15x + x2 = 72.5

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 72.5

Calculate the square root of the right side: 8.514693183

Break this problem into two subproblems by setting 
(x + -7.5) equal to 8.514693183 and -8.514693183.

Subproblem 1

x + -7.5 = 8.514693183 Simplifying x + -7.5 = 8.514693183 Reorder the terms: -7.5 + x = 8.514693183 Solving -7.5 + x = 8.514693183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.514693183 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.514693183 + 7.5 x = 8.514693183 + 7.5 Combine like terms: 8.514693183 + 7.5 = 16.014693183 x = 16.014693183 Simplifying x = 16.014693183

Subproblem 2

x + -7.5 = -8.514693183 Simplifying x + -7.5 = -8.514693183 Reorder the terms: -7.5 + x = -8.514693183 Solving -7.5 + x = -8.514693183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.514693183 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.514693183 + 7.5 x = -8.514693183 + 7.5 Combine like terms: -8.514693183 + 7.5 = -1.014693183 x = -1.014693183 Simplifying x = -1.014693183

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.014693183, -1.014693183}

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