3x^2+26x=-18

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Solution for 3x^2+26x=-18 equation:


Simplifying
3x2 + 26x = -18

Reorder the terms:
26x + 3x2 = -18

Solving
26x + 3x2 = -18

Solving for variable 'x'.

Reorder the terms:
18 + 26x + 3x2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + 26x + 3x2 = 0

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

Divide each side by '3'.
6 + 8.666666667x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 8.666666667x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 8.666666667x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 8.666666667x + x2 = 0 + -6
8.666666667x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
8.666666667x + x2 = -6

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 = -6 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667x + x2 = -6 + 18.77777778

Combine like terms: -6 + 18.77777778 = 12.77777778
18.77777778 + 8.666666667x + x2 = 12.77777778

Factor a perfect square on the left side:
(x + 4.333333334)(x + 4.333333334) = 12.77777778

Calculate the square root of the right side: 3.574601765

Break this problem into two subproblems by setting 
(x + 4.333333334) equal to 3.574601765 and -3.574601765.

Subproblem 1

x + 4.333333334 = 3.574601765 Simplifying x + 4.333333334 = 3.574601765 Reorder the terms: 4.333333334 + x = 3.574601765 Solving 4.333333334 + x = 3.574601765 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 = 3.574601765 + -4.333333334 Combine like terms: 4.333333334 + -4.333333334 = 0.000000000 0.000000000 + x = 3.574601765 + -4.333333334 x = 3.574601765 + -4.333333334 Combine like terms: 3.574601765 + -4.333333334 = -0.758731569 x = -0.758731569 Simplifying x = -0.758731569

Subproblem 2

x + 4.333333334 = -3.574601765 Simplifying x + 4.333333334 = -3.574601765 Reorder the terms: 4.333333334 + x = -3.574601765 Solving 4.333333334 + x = -3.574601765 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 = -3.574601765 + -4.333333334 Combine like terms: 4.333333334 + -4.333333334 = 0.000000000 0.000000000 + x = -3.574601765 + -4.333333334 x = -3.574601765 + -4.333333334 Combine like terms: -3.574601765 + -4.333333334 = -7.907935099 x = -7.907935099 Simplifying x = -7.907935099

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.758731569, -7.907935099}

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