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Simplifying 4x3 + -39x2 + 14x = 0 Reorder the terms: 14x + -39x2 + 4x3 = 0 Solving 14x + -39x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(14 + -39x + 4x2) = 0Subproblem 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 '(14 + -39x + 4x2)' equal to zero and attempt to solve: Simplifying 14 + -39x + 4x2 = 0 Solving 14 + -39x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.5 + -9.75x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -9.75x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -9.75x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -9.75x + x2 = 0 + -3.5 -9.75x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -9.75x + x2 = -3.5 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = -3.5 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = -3.5 + 23.765625 Combine like terms: -3.5 + 23.765625 = 20.265625 23.765625 + -9.75x + x2 = 20.265625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 20.265625 Calculate the square root of the right side: 4.501735776 Break this problem into two subproblems by setting (x + -4.875) equal to 4.501735776 and -4.501735776.Subproblem 1
x + -4.875 = 4.501735776 Simplifying x + -4.875 = 4.501735776 Reorder the terms: -4.875 + x = 4.501735776 Solving -4.875 + x = 4.501735776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 4.501735776 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 4.501735776 + 4.875 x = 4.501735776 + 4.875 Combine like terms: 4.501735776 + 4.875 = 9.376735776 x = 9.376735776 Simplifying x = 9.376735776Subproblem 2
x + -4.875 = -4.501735776 Simplifying x + -4.875 = -4.501735776 Reorder the terms: -4.875 + x = -4.501735776 Solving -4.875 + x = -4.501735776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -4.501735776 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -4.501735776 + 4.875 x = -4.501735776 + 4.875 Combine like terms: -4.501735776 + 4.875 = 0.373264224 x = 0.373264224 Simplifying x = 0.373264224Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.376735776, 0.373264224}Solution
x = {0, 9.376735776, 0.373264224}
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