12x^2+25x-15=0

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Solution for 12x^2+25x-15=0 equation:


Simplifying
12x2 + 25x + -15 = 0

Reorder the terms:
-15 + 25x + 12x2 = 0

Solving
-15 + 25x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-1.25 + 2.083333333x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2.083333333x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2.083333333x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2.083333333x + x2 = 0 + 1.25
2.083333333x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2.083333333x + x2 = 1.25

The x term is 2.083333333x.  Take half its coefficient (1.041666667).
Square it (1.085069445) and add it to both sides.

Add '1.085069445' to each side of the equation.
2.083333333x + 1.085069445 + x2 = 1.25 + 1.085069445

Reorder the terms:
1.085069445 + 2.083333333x + x2 = 1.25 + 1.085069445

Combine like terms: 1.25 + 1.085069445 = 2.335069445
1.085069445 + 2.083333333x + x2 = 2.335069445

Factor a perfect square on the left side:
(x + 1.041666667)(x + 1.041666667) = 2.335069445

Calculate the square root of the right side: 1.528093402

Break this problem into two subproblems by setting 
(x + 1.041666667) equal to 1.528093402 and -1.528093402.

Subproblem 1

x + 1.041666667 = 1.528093402 Simplifying x + 1.041666667 = 1.528093402 Reorder the terms: 1.041666667 + x = 1.528093402 Solving 1.041666667 + x = 1.528093402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + x = 1.528093402 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + x = 1.528093402 + -1.041666667 x = 1.528093402 + -1.041666667 Combine like terms: 1.528093402 + -1.041666667 = 0.486426735 x = 0.486426735 Simplifying x = 0.486426735

Subproblem 2

x + 1.041666667 = -1.528093402 Simplifying x + 1.041666667 = -1.528093402 Reorder the terms: 1.041666667 + x = -1.528093402 Solving 1.041666667 + x = -1.528093402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + x = -1.528093402 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + x = -1.528093402 + -1.041666667 x = -1.528093402 + -1.041666667 Combine like terms: -1.528093402 + -1.041666667 = -2.569760069 x = -2.569760069 Simplifying x = -2.569760069

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.486426735, -2.569760069}

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