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Simplifying 32x3 + 35x2 + -25x = 0 Reorder the terms: -25x + 35x2 + 32x3 = 0 Solving -25x + 35x2 + 32x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-25 + 35x + 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 '(-25 + 35x + 32x2)' equal to zero and attempt to solve: Simplifying -25 + 35x + 32x2 = 0 Solving -25 + 35x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.78125 + 1.09375x + x2 = 0 Move the constant term to the right: Add '0.78125' to each side of the equation. -0.78125 + 1.09375x + 0.78125 + x2 = 0 + 0.78125 Reorder the terms: -0.78125 + 0.78125 + 1.09375x + x2 = 0 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + 1.09375x + x2 = 0 + 0.78125 1.09375x + x2 = 0 + 0.78125 Combine like terms: 0 + 0.78125 = 0.78125 1.09375x + x2 = 0.78125 The x term is 1.09375x. Take half its coefficient (0.546875). Square it (0.2990722656) and add it to both sides. Add '0.2990722656' to each side of the equation. 1.09375x + 0.2990722656 + x2 = 0.78125 + 0.2990722656 Reorder the terms: 0.2990722656 + 1.09375x + x2 = 0.78125 + 0.2990722656 Combine like terms: 0.78125 + 0.2990722656 = 1.0803222656 0.2990722656 + 1.09375x + x2 = 1.0803222656 Factor a perfect square on the left side: (x + 0.546875)(x + 0.546875) = 1.0803222656 Calculate the square root of the right side: 1.039385523 Break this problem into two subproblems by setting (x + 0.546875) equal to 1.039385523 and -1.039385523.Subproblem 1
x + 0.546875 = 1.039385523 Simplifying x + 0.546875 = 1.039385523 Reorder the terms: 0.546875 + x = 1.039385523 Solving 0.546875 + x = 1.039385523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.546875' to each side of the equation. 0.546875 + -0.546875 + x = 1.039385523 + -0.546875 Combine like terms: 0.546875 + -0.546875 = 0.000000 0.000000 + x = 1.039385523 + -0.546875 x = 1.039385523 + -0.546875 Combine like terms: 1.039385523 + -0.546875 = 0.492510523 x = 0.492510523 Simplifying x = 0.492510523Subproblem 2
x + 0.546875 = -1.039385523 Simplifying x + 0.546875 = -1.039385523 Reorder the terms: 0.546875 + x = -1.039385523 Solving 0.546875 + x = -1.039385523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.546875' to each side of the equation. 0.546875 + -0.546875 + x = -1.039385523 + -0.546875 Combine like terms: 0.546875 + -0.546875 = 0.000000 0.000000 + x = -1.039385523 + -0.546875 x = -1.039385523 + -0.546875 Combine like terms: -1.039385523 + -0.546875 = -1.586260523 x = -1.586260523 Simplifying x = -1.586260523Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.492510523, -1.586260523}Solution
x = {0, 0.492510523, -1.586260523}
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