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Simplifying 4x3 + -15x2 + 12x = 0 Reorder the terms: 12x + -15x2 + 4x3 = 0 Solving 12x + -15x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(12 + -15x + 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 '(12 + -15x + 4x2)' equal to zero and attempt to solve: Simplifying 12 + -15x + 4x2 = 0 Solving 12 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + -3.75x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -3.75x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -3.75x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -3.75x + x2 = 0 + -3 -3.75x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -3.75x + x2 = -3 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = -3 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = -3 + 3.515625 Combine like terms: -3 + 3.515625 = 0.515625 3.515625 + -3.75x + x2 = 0.515625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + -1.875) equal to 0.718070331 and -0.718070331.Subproblem 1
x + -1.875 = 0.718070331 Simplifying x + -1.875 = 0.718070331 Reorder the terms: -1.875 + x = 0.718070331 Solving -1.875 + x = 0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 0.718070331 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 0.718070331 + 1.875 x = 0.718070331 + 1.875 Combine like terms: 0.718070331 + 1.875 = 2.593070331 x = 2.593070331 Simplifying x = 2.593070331Subproblem 2
x + -1.875 = -0.718070331 Simplifying x + -1.875 = -0.718070331 Reorder the terms: -1.875 + x = -0.718070331 Solving -1.875 + x = -0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -0.718070331 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -0.718070331 + 1.875 x = -0.718070331 + 1.875 Combine like terms: -0.718070331 + 1.875 = 1.156929669 x = 1.156929669 Simplifying x = 1.156929669Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.593070331, 1.156929669}Solution
x = {0, 2.593070331, 1.156929669}
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