2x^2+15x-12=1

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Solution for 2x^2+15x-12=1 equation:


Simplifying
2x2 + 15x + -12 = 1

Reorder the terms:
-12 + 15x + 2x2 = 1

Solving
-12 + 15x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-12 + -1 + 15x + 2x2 = 1 + -1

Combine like terms: -12 + -1 = -13
-13 + 15x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-13 + 15x + 2x2 = 0

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

Divide each side by '2'.
-6.5 + 7.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 7.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 7.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 7.5x + x2 = 0 + 6.5
7.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
7.5x + x2 = 6.5

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 6.5 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 6.5 + 14.0625

Combine like terms: 6.5 + 14.0625 = 20.5625
14.0625 + 7.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + 3.75) equal to 4.534589287 and -4.534589287.

Subproblem 1

x + 3.75 = 4.534589287 Simplifying x + 3.75 = 4.534589287 Reorder the terms: 3.75 + x = 4.534589287 Solving 3.75 + x = 4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 4.534589287 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.534589287 + -3.75 x = 4.534589287 + -3.75 Combine like terms: 4.534589287 + -3.75 = 0.784589287 x = 0.784589287 Simplifying x = 0.784589287

Subproblem 2

x + 3.75 = -4.534589287 Simplifying x + 3.75 = -4.534589287 Reorder the terms: 3.75 + x = -4.534589287 Solving 3.75 + x = -4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -4.534589287 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.534589287 + -3.75 x = -4.534589287 + -3.75 Combine like terms: -4.534589287 + -3.75 = -8.284589287 x = -8.284589287 Simplifying x = -8.284589287

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.784589287, -8.284589287}

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