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Simplifying 18x2 + -48x + -16 = 0 Reorder the terms: -16 + -48x + 18x2 = 0 Solving -16 + -48x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -24x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -24x + 9x2)' equal to zero and attempt to solve: Simplifying -8 + -24x + 9x2 = 0 Solving -8 + -24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -2.666666667x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -2.666666667x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + 0.8888888889 -2.666666667x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -2.666666667x + x2 = 0.8888888889 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 0.8888888889 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.8888888889 + 1.777777780 Combine like terms: 0.8888888889 + 1.777777780 = 2.6666666689 1.777777780 + -2.666666667x + x2 = 2.6666666689 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 2.6666666689 Calculate the square root of the right side: 1.632993163 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.632993163 and -1.632993163.Subproblem 1
x + -1.333333334 = 1.632993163 Simplifying x + -1.333333334 = 1.632993163 Reorder the terms: -1.333333334 + x = 1.632993163 Solving -1.333333334 + x = 1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.632993163 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.632993163 + 1.333333334 x = 1.632993163 + 1.333333334 Combine like terms: 1.632993163 + 1.333333334 = 2.966326497 x = 2.966326497 Simplifying x = 2.966326497Subproblem 2
x + -1.333333334 = -1.632993163 Simplifying x + -1.333333334 = -1.632993163 Reorder the terms: -1.333333334 + x = -1.632993163 Solving -1.333333334 + x = -1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.632993163 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.632993163 + 1.333333334 x = -1.632993163 + 1.333333334 Combine like terms: -1.632993163 + 1.333333334 = -0.299659829 x = -0.299659829 Simplifying x = -0.299659829Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.966326497, -0.299659829}Solution
x = {2.966326497, -0.299659829}
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