15x^2-7x-2=12

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Solution for 15x^2-7x-2=12 equation:


Simplifying
15x2 + -7x + -2 = 12

Reorder the terms:
-2 + -7x + 15x2 = 12

Solving
-2 + -7x + 15x2 = 12

Solving for variable 'x'.

Reorder the terms:
-2 + -12 + -7x + 15x2 = 12 + -12

Combine like terms: -2 + -12 = -14
-14 + -7x + 15x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-14 + -7x + 15x2 = 0

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

Divide each side by '15'.
-0.9333333333 + -0.4666666667x + x2 = 0

Move the constant term to the right:

Add '0.9333333333' to each side of the equation.
-0.9333333333 + -0.4666666667x + 0.9333333333 + x2 = 0 + 0.9333333333

Reorder the terms:
-0.9333333333 + 0.9333333333 + -0.4666666667x + x2 = 0 + 0.9333333333

Combine like terms: -0.9333333333 + 0.9333333333 = 0.0000000000
0.0000000000 + -0.4666666667x + x2 = 0 + 0.9333333333
-0.4666666667x + x2 = 0 + 0.9333333333

Combine like terms: 0 + 0.9333333333 = 0.9333333333
-0.4666666667x + x2 = 0.9333333333

The x term is -0.4666666667x.  Take half its coefficient (-0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
-0.4666666667x + 0.05444444448 + x2 = 0.9333333333 + 0.05444444448

Reorder the terms:
0.05444444448 + -0.4666666667x + x2 = 0.9333333333 + 0.05444444448

Combine like terms: 0.9333333333 + 0.05444444448 = 0.98777777778
0.05444444448 + -0.4666666667x + x2 = 0.98777777778

Factor a perfect square on the left side:
(x + -0.2333333334)(x + -0.2333333334) = 0.98777777778

Calculate the square root of the right side: 0.993870101

Break this problem into two subproblems by setting 
(x + -0.2333333334) equal to 0.993870101 and -0.993870101.

Subproblem 1

x + -0.2333333334 = 0.993870101 Simplifying x + -0.2333333334 = 0.993870101 Reorder the terms: -0.2333333334 + x = 0.993870101 Solving -0.2333333334 + x = 0.993870101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = 0.993870101 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = 0.993870101 + 0.2333333334 x = 0.993870101 + 0.2333333334 Combine like terms: 0.993870101 + 0.2333333334 = 1.2272034344 x = 1.2272034344 Simplifying x = 1.2272034344

Subproblem 2

x + -0.2333333334 = -0.993870101 Simplifying x + -0.2333333334 = -0.993870101 Reorder the terms: -0.2333333334 + x = -0.993870101 Solving -0.2333333334 + x = -0.993870101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = -0.993870101 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = -0.993870101 + 0.2333333334 x = -0.993870101 + 0.2333333334 Combine like terms: -0.993870101 + 0.2333333334 = -0.7605367676 x = -0.7605367676 Simplifying x = -0.7605367676

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2272034344, -0.7605367676}

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