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Simplifying x(4x2 + -38x + -32) = 0 Reorder the terms: x(-32 + -38x + 4x2) = 0 (-32 * x + -38x * x + 4x2 * x) = 0 (-32x + -38x2 + 4x3) = 0 Solving -32x + -38x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-16 + -19x + 2x2) = 0 Ignore the factor 2.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 '(-16 + -19x + 2x2)' equal to zero and attempt to solve: Simplifying -16 + -19x + 2x2 = 0 Solving -16 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -9.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -9.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -9.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9.5x + x2 = 0 + 8 -9.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -9.5x + x2 = 8 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 8 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 8 + 22.5625 Combine like terms: 8 + 22.5625 = 30.5625 22.5625 + -9.5x + x2 = 30.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + -4.75) equal to 5.528336097 and -5.528336097.Subproblem 1
x + -4.75 = 5.528336097 Simplifying x + -4.75 = 5.528336097 Reorder the terms: -4.75 + x = 5.528336097 Solving -4.75 + x = 5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 5.528336097 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.528336097 + 4.75 x = 5.528336097 + 4.75 Combine like terms: 5.528336097 + 4.75 = 10.278336097 x = 10.278336097 Simplifying x = 10.278336097Subproblem 2
x + -4.75 = -5.528336097 Simplifying x + -4.75 = -5.528336097 Reorder the terms: -4.75 + x = -5.528336097 Solving -4.75 + x = -5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -5.528336097 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.528336097 + 4.75 x = -5.528336097 + 4.75 Combine like terms: -5.528336097 + 4.75 = -0.778336097 x = -0.778336097 Simplifying x = -0.778336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.278336097, -0.778336097}Solution
x = {0, 10.278336097, -0.778336097}
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