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Simplifying 9x2 = 24x + -9 Reorder the terms: 9x2 = -9 + 24x Solving 9x2 = -9 + 24x Solving for variable 'x'. Reorder the terms: 9 + -24x + 9x2 = -9 + 24x + 9 + -24x Reorder the terms: 9 + -24x + 9x2 = -9 + 9 + 24x + -24x Combine like terms: -9 + 9 = 0 9 + -24x + 9x2 = 0 + 24x + -24x 9 + -24x + 9x2 = 24x + -24x Combine like terms: 24x + -24x = 0 9 + -24x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -8x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -8x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + -8x + 3x2 = 0 Solving 3 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.666666667x + x2 = 0 + -1 -2.666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.666666667x + x2 = -1 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 = -1 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -1 + 1.777777780 Combine like terms: -1 + 1.777777780 = 0.77777778 1.777777780 + -2.666666667x + x2 = 0.77777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 0.77777778 Calculate the square root of the right side: 0.881917105 Break this problem into two subproblems by setting (x + -1.333333334) equal to 0.881917105 and -0.881917105.Subproblem 1
x + -1.333333334 = 0.881917105 Simplifying x + -1.333333334 = 0.881917105 Reorder the terms: -1.333333334 + x = 0.881917105 Solving -1.333333334 + x = 0.881917105 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 = 0.881917105 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 0.881917105 + 1.333333334 x = 0.881917105 + 1.333333334 Combine like terms: 0.881917105 + 1.333333334 = 2.215250439 x = 2.215250439 Simplifying x = 2.215250439Subproblem 2
x + -1.333333334 = -0.881917105 Simplifying x + -1.333333334 = -0.881917105 Reorder the terms: -1.333333334 + x = -0.881917105 Solving -1.333333334 + x = -0.881917105 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 = -0.881917105 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -0.881917105 + 1.333333334 x = -0.881917105 + 1.333333334 Combine like terms: -0.881917105 + 1.333333334 = 0.451416229 x = 0.451416229 Simplifying x = 0.451416229Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.215250439, 0.451416229}Solution
x = {2.215250439, 0.451416229}
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