25x^2+60x-12=0

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Solution for 25x^2+60x-12=0 equation:


Simplifying
25x2 + 60x + -12 = 0

Reorder the terms:
-12 + 60x + 25x2 = 0

Solving
-12 + 60x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-0.48 + 2.4x + x2 = 0

Move the constant term to the right:

Add '0.48' to each side of the equation.
-0.48 + 2.4x + 0.48 + x2 = 0 + 0.48

Reorder the terms:
-0.48 + 0.48 + 2.4x + x2 = 0 + 0.48

Combine like terms: -0.48 + 0.48 = 0.00
0.00 + 2.4x + x2 = 0 + 0.48
2.4x + x2 = 0 + 0.48

Combine like terms: 0 + 0.48 = 0.48
2.4x + x2 = 0.48

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 0.48 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 0.48 + 1.44

Combine like terms: 0.48 + 1.44 = 1.92
1.44 + 2.4x + x2 = 1.92

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 1.92

Calculate the square root of the right side: 1.385640646

Break this problem into two subproblems by setting 
(x + 1.2) equal to 1.385640646 and -1.385640646.

Subproblem 1

x + 1.2 = 1.385640646 Simplifying x + 1.2 = 1.385640646 Reorder the terms: 1.2 + x = 1.385640646 Solving 1.2 + x = 1.385640646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.385640646 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.385640646 + -1.2 x = 1.385640646 + -1.2 Combine like terms: 1.385640646 + -1.2 = 0.185640646 x = 0.185640646 Simplifying x = 0.185640646

Subproblem 2

x + 1.2 = -1.385640646 Simplifying x + 1.2 = -1.385640646 Reorder the terms: 1.2 + x = -1.385640646 Solving 1.2 + x = -1.385640646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.385640646 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.385640646 + -1.2 x = -1.385640646 + -1.2 Combine like terms: -1.385640646 + -1.2 = -2.585640646 x = -2.585640646 Simplifying x = -2.585640646

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.185640646, -2.585640646}

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