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Simplifying -15x3 + 40x2 + 35x = 0 Reorder the terms: 35x + 40x2 + -15x3 = 0 Solving 35x + 40x2 + -15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(7 + 8x + -3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + 8x + -3x2)' equal to zero and attempt to solve: Simplifying 7 + 8x + -3x2 = 0 Solving 7 + 8x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.333333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -2.666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -2.666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 2.333333333 -2.666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -2.666666667x + x2 = 2.333333333 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 = 2.333333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 2.333333333 + 1.777777780 Combine like terms: 2.333333333 + 1.777777780 = 4.111111113 1.777777780 + -2.666666667x + x2 = 4.111111113 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 4.111111113 Calculate the square root of the right side: 2.027587511 Break this problem into two subproblems by setting (x + -1.333333334) equal to 2.027587511 and -2.027587511.Subproblem 1
x + -1.333333334 = 2.027587511 Simplifying x + -1.333333334 = 2.027587511 Reorder the terms: -1.333333334 + x = 2.027587511 Solving -1.333333334 + x = 2.027587511 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 = 2.027587511 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.027587511 + 1.333333334 x = 2.027587511 + 1.333333334 Combine like terms: 2.027587511 + 1.333333334 = 3.360920845 x = 3.360920845 Simplifying x = 3.360920845Subproblem 2
x + -1.333333334 = -2.027587511 Simplifying x + -1.333333334 = -2.027587511 Reorder the terms: -1.333333334 + x = -2.027587511 Solving -1.333333334 + x = -2.027587511 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 = -2.027587511 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.027587511 + 1.333333334 x = -2.027587511 + 1.333333334 Combine like terms: -2.027587511 + 1.333333334 = -0.694254177 x = -0.694254177 Simplifying x = -0.694254177Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.360920845, -0.694254177}Solution
x = {0, 3.360920845, -0.694254177}
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