0=-3x^2-26x-15

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Solution for 0=-3x^2-26x-15 equation:


Simplifying
0 = -3x2 + -26x + -15

Reorder the terms:
0 = -15 + -26x + -3x2

Solving
0 = -15 + -26x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + 26x + 3x2 = -15 + -26x + -3x2 + 15 + 26x + 3x2

Reorder the terms:
15 + 26x + 3x2 = -15 + 15 + -26x + 26x + -3x2 + 3x2

Combine like terms: -15 + 15 = 0
15 + 26x + 3x2 = 0 + -26x + 26x + -3x2 + 3x2
15 + 26x + 3x2 = -26x + 26x + -3x2 + 3x2

Combine like terms: -26x + 26x = 0
15 + 26x + 3x2 = 0 + -3x2 + 3x2
15 + 26x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
15 + 26x + 3x2 = 0

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

Divide each side by '3'.
5 + 8.666666667x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8.666666667x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 8.666666667x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8.666666667x + x2 = 0 + -5
8.666666667x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
8.666666667x + x2 = -5

The x term is 8.666666667x.  Take half its coefficient (4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
8.666666667x + 18.77777778 + x2 = -5 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667x + x2 = -5 + 18.77777778

Combine like terms: -5 + 18.77777778 = 13.77777778
18.77777778 + 8.666666667x + x2 = 13.77777778

Factor a perfect square on the left side:
(x + 4.333333334)(x + 4.333333334) = 13.77777778

Calculate the square root of the right side: 3.711842909

Break this problem into two subproblems by setting 
(x + 4.333333334) equal to 3.711842909 and -3.711842909.

Subproblem 1

x + 4.333333334 = 3.711842909 Simplifying x + 4.333333334 = 3.711842909 Reorder the terms: 4.333333334 + x = 3.711842909 Solving 4.333333334 + x = 3.711842909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.333333334' to each side of the equation. 4.333333334 + -4.333333334 + x = 3.711842909 + -4.333333334 Combine like terms: 4.333333334 + -4.333333334 = 0.000000000 0.000000000 + x = 3.711842909 + -4.333333334 x = 3.711842909 + -4.333333334 Combine like terms: 3.711842909 + -4.333333334 = -0.621490425 x = -0.621490425 Simplifying x = -0.621490425

Subproblem 2

x + 4.333333334 = -3.711842909 Simplifying x + 4.333333334 = -3.711842909 Reorder the terms: 4.333333334 + x = -3.711842909 Solving 4.333333334 + x = -3.711842909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.333333334' to each side of the equation. 4.333333334 + -4.333333334 + x = -3.711842909 + -4.333333334 Combine like terms: 4.333333334 + -4.333333334 = 0.000000000 0.000000000 + x = -3.711842909 + -4.333333334 x = -3.711842909 + -4.333333334 Combine like terms: -3.711842909 + -4.333333334 = -8.045176243 x = -8.045176243 Simplifying x = -8.045176243

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.621490425, -8.045176243}

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