2x^2-60x-45=0

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Solution for 2x^2-60x-45=0 equation:


Simplifying
2x2 + -60x + -45 = 0

Reorder the terms:
-45 + -60x + 2x2 = 0

Solving
-45 + -60x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-22.5 + -30x + x2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + -30x + 22.5 + x2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + -30x + x2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + -30x + x2 = 0 + 22.5
-30x + x2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
-30x + x2 = 22.5

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 22.5 + 225

Reorder the terms:
225 + -30x + x2 = 22.5 + 225

Combine like terms: 22.5 + 225 = 247.5
225 + -30x + x2 = 247.5

Factor a perfect square on the left side:
(x + -15)(x + -15) = 247.5

Calculate the square root of the right side: 15.732132723

Break this problem into two subproblems by setting 
(x + -15) equal to 15.732132723 and -15.732132723.

Subproblem 1

x + -15 = 15.732132723 Simplifying x + -15 = 15.732132723 Reorder the terms: -15 + x = 15.732132723 Solving -15 + x = 15.732132723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 15.732132723 + 15 Combine like terms: -15 + 15 = 0 0 + x = 15.732132723 + 15 x = 15.732132723 + 15 Combine like terms: 15.732132723 + 15 = 30.732132723 x = 30.732132723 Simplifying x = 30.732132723

Subproblem 2

x + -15 = -15.732132723 Simplifying x + -15 = -15.732132723 Reorder the terms: -15 + x = -15.732132723 Solving -15 + x = -15.732132723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -15.732132723 + 15 Combine like terms: -15 + 15 = 0 0 + x = -15.732132723 + 15 x = -15.732132723 + 15 Combine like terms: -15.732132723 + 15 = -0.732132723 x = -0.732132723 Simplifying x = -0.732132723

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.732132723, -0.732132723}

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