2x^2+15x-5.9=0

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Solution for 2x^2+15x-5.9=0 equation:


Simplifying
2x2 + 15x + -5.9 = 0

Reorder the terms:
-5.9 + 15x + 2x2 = 0

Solving
-5.9 + 15x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-2.95 + 7.5x + x2 = 0

Move the constant term to the right:

Add '2.95' to each side of the equation.
-2.95 + 7.5x + 2.95 + x2 = 0 + 2.95

Reorder the terms:
-2.95 + 2.95 + 7.5x + x2 = 0 + 2.95

Combine like terms: -2.95 + 2.95 = 0.00
0.00 + 7.5x + x2 = 0 + 2.95
7.5x + x2 = 0 + 2.95

Combine like terms: 0 + 2.95 = 2.95
7.5x + x2 = 2.95

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 = 2.95 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 2.95 + 14.0625

Combine like terms: 2.95 + 14.0625 = 17.0125
14.0625 + 7.5x + x2 = 17.0125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 17.0125

Calculate the square root of the right side: 4.124621195

Break this problem into two subproblems by setting 
(x + 3.75) equal to 4.124621195 and -4.124621195.

Subproblem 1

x + 3.75 = 4.124621195 Simplifying x + 3.75 = 4.124621195 Reorder the terms: 3.75 + x = 4.124621195 Solving 3.75 + x = 4.124621195 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 = 4.124621195 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.124621195 + -3.75 x = 4.124621195 + -3.75 Combine like terms: 4.124621195 + -3.75 = 0.374621195 x = 0.374621195 Simplifying x = 0.374621195

Subproblem 2

x + 3.75 = -4.124621195 Simplifying x + 3.75 = -4.124621195 Reorder the terms: 3.75 + x = -4.124621195 Solving 3.75 + x = -4.124621195 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 = -4.124621195 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.124621195 + -3.75 x = -4.124621195 + -3.75 Combine like terms: -4.124621195 + -3.75 = -7.874621195 x = -7.874621195 Simplifying x = -7.874621195

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.374621195, -7.874621195}

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