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Simplifying -2x3 + 3x2 + 72x = 0 Reorder the terms: 72x + 3x2 + -2x3 = 0 Solving 72x + 3x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(72 + 3x + -2x2) = 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 '(72 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying 72 + 3x + -2x2 = 0 Solving 72 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -36 + -1.5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -1.5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -1.5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1.5x + x2 = 0 + 36 -1.5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1.5x + x2 = 36 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 36 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 36 + 0.5625 Combine like terms: 36 + 0.5625 = 36.5625 0.5625 + -1.5x + x2 = 36.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (x + -0.75) equal to 6.046693311 and -6.046693311.Subproblem 1
x + -0.75 = 6.046693311 Simplifying x + -0.75 = 6.046693311 Reorder the terms: -0.75 + x = 6.046693311 Solving -0.75 + x = 6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 6.046693311 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 6.046693311 + 0.75 x = 6.046693311 + 0.75 Combine like terms: 6.046693311 + 0.75 = 6.796693311 x = 6.796693311 Simplifying x = 6.796693311Subproblem 2
x + -0.75 = -6.046693311 Simplifying x + -0.75 = -6.046693311 Reorder the terms: -0.75 + x = -6.046693311 Solving -0.75 + x = -6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -6.046693311 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -6.046693311 + 0.75 x = -6.046693311 + 0.75 Combine like terms: -6.046693311 + 0.75 = -5.296693311 x = -5.296693311 Simplifying x = -5.296693311Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.796693311, -5.296693311}Solution
x = {0, 6.796693311, -5.296693311}
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