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Simplifying -5x3 + 5x2 + 12x = 0 Reorder the terms: 12x + 5x2 + -5x3 = 0 Solving 12x + 5x2 + -5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(12 + 5x + -5x2) = 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 + 5x + -5x2)' equal to zero and attempt to solve: Simplifying 12 + 5x + -5x2 = 0 Solving 12 + 5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + -1x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -1x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -1x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -1x + x2 = 0 + 2.4 -1x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -1x + x2 = 2.4 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.4 + 0.25 Combine like terms: 2.4 + 0.25 = 2.65 0.25 + -1x + x2 = 2.65 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.65 Calculate the square root of the right side: 1.62788206 Break this problem into two subproblems by setting (x + -0.5) equal to 1.62788206 and -1.62788206.Subproblem 1
x + -0.5 = 1.62788206 Simplifying x + -0.5 = 1.62788206 Reorder the terms: -0.5 + x = 1.62788206 Solving -0.5 + x = 1.62788206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.62788206 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.62788206 + 0.5 x = 1.62788206 + 0.5 Combine like terms: 1.62788206 + 0.5 = 2.12788206 x = 2.12788206 Simplifying x = 2.12788206Subproblem 2
x + -0.5 = -1.62788206 Simplifying x + -0.5 = -1.62788206 Reorder the terms: -0.5 + x = -1.62788206 Solving -0.5 + x = -1.62788206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.62788206 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.62788206 + 0.5 x = -1.62788206 + 0.5 Combine like terms: -1.62788206 + 0.5 = -1.12788206 x = -1.12788206 Simplifying x = -1.12788206Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.12788206, -1.12788206}Solution
x = {0, 2.12788206, -1.12788206}
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