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Simplifying 32x3 + 19x2 + -72x = 0 Reorder the terms: -72x + 19x2 + 32x3 = 0 Solving -72x + 19x2 + 32x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-72 + 19x + 32x2) = 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 + 19x + 32x2)' equal to zero and attempt to solve: Simplifying -72 + 19x + 32x2 = 0 Solving -72 + 19x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -2.25 + 0.59375x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.59375x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.59375x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.59375x + x2 = 0 + 2.25 0.59375x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.59375x + x2 = 2.25 The x term is 0.59375x. Take half its coefficient (0.296875). Square it (0.08813476563) and add it to both sides. Add '0.08813476563' to each side of the equation. 0.59375x + 0.08813476563 + x2 = 2.25 + 0.08813476563 Reorder the terms: 0.08813476563 + 0.59375x + x2 = 2.25 + 0.08813476563 Combine like terms: 2.25 + 0.08813476563 = 2.33813476563 0.08813476563 + 0.59375x + x2 = 2.33813476563 Factor a perfect square on the left side: (x + 0.296875)(x + 0.296875) = 2.33813476563 Calculate the square root of the right side: 1.529096062 Break this problem into two subproblems by setting (x + 0.296875) equal to 1.529096062 and -1.529096062.Subproblem 1
x + 0.296875 = 1.529096062 Simplifying x + 0.296875 = 1.529096062 Reorder the terms: 0.296875 + x = 1.529096062 Solving 0.296875 + x = 1.529096062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.296875' to each side of the equation. 0.296875 + -0.296875 + x = 1.529096062 + -0.296875 Combine like terms: 0.296875 + -0.296875 = 0.000000 0.000000 + x = 1.529096062 + -0.296875 x = 1.529096062 + -0.296875 Combine like terms: 1.529096062 + -0.296875 = 1.232221062 x = 1.232221062 Simplifying x = 1.232221062Subproblem 2
x + 0.296875 = -1.529096062 Simplifying x + 0.296875 = -1.529096062 Reorder the terms: 0.296875 + x = -1.529096062 Solving 0.296875 + x = -1.529096062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.296875' to each side of the equation. 0.296875 + -0.296875 + x = -1.529096062 + -0.296875 Combine like terms: 0.296875 + -0.296875 = 0.000000 0.000000 + x = -1.529096062 + -0.296875 x = -1.529096062 + -0.296875 Combine like terms: -1.529096062 + -0.296875 = -1.825971062 x = -1.825971062 Simplifying x = -1.825971062Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.232221062, -1.825971062}Solution
x = {0, 1.232221062, -1.825971062}
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