6x^2+22x-18=0

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Solution for 6x^2+22x-18=0 equation:


Simplifying
6x2 + 22x + -18 = 0

Reorder the terms:
-18 + 22x + 6x2 = 0

Solving
-18 + 22x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 11x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + 11x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + 11x + 3x2 = 0 Solving -9 + 11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 3.666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.666666667x + x2 = 0 + 3 3.666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.666666667x + x2 = 3 The x term is 3.666666667x. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667x + 3.361111114 + x2 = 3 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 3 + 3.361111114 Combine like terms: 3 + 3.361111114 = 6.361111114 3.361111114 + 3.666666667x + x2 = 6.361111114 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 6.361111114 Calculate the square root of the right side: 2.522124326 Break this problem into two subproblems by setting (x + 1.833333334) equal to 2.522124326 and -2.522124326.

Subproblem 1

x + 1.833333334 = 2.522124326 Simplifying x + 1.833333334 = 2.522124326 Reorder the terms: 1.833333334 + x = 2.522124326 Solving 1.833333334 + x = 2.522124326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 2.522124326 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 2.522124326 + -1.833333334 x = 2.522124326 + -1.833333334 Combine like terms: 2.522124326 + -1.833333334 = 0.688790992 x = 0.688790992 Simplifying x = 0.688790992

Subproblem 2

x + 1.833333334 = -2.522124326 Simplifying x + 1.833333334 = -2.522124326 Reorder the terms: 1.833333334 + x = -2.522124326 Solving 1.833333334 + x = -2.522124326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -2.522124326 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -2.522124326 + -1.833333334 x = -2.522124326 + -1.833333334 Combine like terms: -2.522124326 + -1.833333334 = -4.35545766 x = -4.35545766 Simplifying x = -4.35545766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.688790992, -4.35545766}

Solution

x = {0.688790992, -4.35545766}

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