-2.5x^2+25x-60=0

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Solution for -2.5x^2+25x-60=0 equation:


Simplifying
-2.5x2 + 25x + -60 = 0

Reorder the terms:
-60 + 25x + -2.5x2 = 0

Solving
-60 + 25x + -2.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2.5 the coefficient of the squared term: 

Divide each side by '-2.5'.
24 + -10x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -10x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -10x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -10x + x2 = 0 + -24
-10x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-10x + x2 = -24

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -24 + 25

Reorder the terms:
25 + -10x + x2 = -24 + 25

Combine like terms: -24 + 25 = 1
25 + -10x + x2 = 1

Factor a perfect square on the left side:
(x + -5)(x + -5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + -5) equal to 1 and -1.

Subproblem 1

x + -5 = 1 Simplifying x + -5 = 1 Reorder the terms: -5 + x = 1 Solving -5 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1 + 5 x = 1 + 5 Combine like terms: 1 + 5 = 6 x = 6 Simplifying x = 6

Subproblem 2

x + -5 = -1 Simplifying x + -5 = -1 Reorder the terms: -5 + x = -1 Solving -5 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1 + 5 x = -1 + 5 Combine like terms: -1 + 5 = 4 x = 4 Simplifying x = 4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6, 4}

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