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Simplifying 36x2 + 24x + -18 = 0 Reorder the terms: -18 + 24x + 36x2 = 0 Solving -18 + 24x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 4x + 6x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + 4x + 6x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + 6x2 = 0 Solving -3 + 4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.6666666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.6666666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.6666666667x + x2 = 0 + 0.5 0.6666666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.6666666667x + x2 = 0.5 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.5 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.5 + 0.1111111112 Combine like terms: 0.5 + 0.1111111112 = 0.6111111112 0.1111111112 + 0.6666666667x + x2 = 0.6111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.6111111112 Calculate the square root of the right side: 0.78173596 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.78173596 and -0.78173596.Subproblem 1
x + 0.3333333334 = 0.78173596 Simplifying x + 0.3333333334 = 0.78173596 Reorder the terms: 0.3333333334 + x = 0.78173596 Solving 0.3333333334 + x = 0.78173596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.78173596 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.78173596 + -0.3333333334 x = 0.78173596 + -0.3333333334 Combine like terms: 0.78173596 + -0.3333333334 = 0.4484026266 x = 0.4484026266 Simplifying x = 0.4484026266Subproblem 2
x + 0.3333333334 = -0.78173596 Simplifying x + 0.3333333334 = -0.78173596 Reorder the terms: 0.3333333334 + x = -0.78173596 Solving 0.3333333334 + x = -0.78173596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.78173596 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.78173596 + -0.3333333334 x = -0.78173596 + -0.3333333334 Combine like terms: -0.78173596 + -0.3333333334 = -1.1150692934 x = -1.1150692934 Simplifying x = -1.1150692934Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4484026266, -1.1150692934}Solution
x = {0.4484026266, -1.1150692934}
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