12x^2+15x-25=0

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


Simplifying
12x2 + 15x + -25 = 0

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

Solving
-25 + 15x + 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'.
-2.083333333 + 1.25x + x2 = 0

Move the constant term to the right:

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

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

Combine like terms: -2.083333333 + 2.083333333 = 0.000000000
0.000000000 + 1.25x + x2 = 0 + 2.083333333
1.25x + x2 = 0 + 2.083333333

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

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 2.083333333 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 2.083333333 + 0.390625

Combine like terms: 2.083333333 + 0.390625 = 2.473958333
0.390625 + 1.25x + x2 = 2.473958333

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 2.473958333

Calculate the square root of the right side: 1.572882174

Break this problem into two subproblems by setting 
(x + 0.625) equal to 1.572882174 and -1.572882174.

Subproblem 1

x + 0.625 = 1.572882174 Simplifying x + 0.625 = 1.572882174 Reorder the terms: 0.625 + x = 1.572882174 Solving 0.625 + x = 1.572882174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.572882174 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.572882174 + -0.625 x = 1.572882174 + -0.625 Combine like terms: 1.572882174 + -0.625 = 0.947882174 x = 0.947882174 Simplifying x = 0.947882174

Subproblem 2

x + 0.625 = -1.572882174 Simplifying x + 0.625 = -1.572882174 Reorder the terms: 0.625 + x = -1.572882174 Solving 0.625 + x = -1.572882174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.572882174 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.572882174 + -0.625 x = -1.572882174 + -0.625 Combine like terms: -1.572882174 + -0.625 = -2.197882174 x = -2.197882174 Simplifying x = -2.197882174

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.947882174, -2.197882174}

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