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Simplifying 8x3 + 14x2 + -16x = 0 Reorder the terms: -16x + 14x2 + 8x3 = 0 Solving -16x + 14x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-8 + 7x + 4x2) = 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 '(-8 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying -8 + 7x + 4x2 = 0 Solving -8 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 1.75x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.75x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 1.75x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.75x + x2 = 0 + 2 1.75x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.75x + x2 = 2 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 2 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 2 + 0.765625 Combine like terms: 2 + 0.765625 = 2.765625 0.765625 + 1.75x + x2 = 2.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (x + 0.875) equal to 1.663016837 and -1.663016837.Subproblem 1
x + 0.875 = 1.663016837 Simplifying x + 0.875 = 1.663016837 Reorder the terms: 0.875 + x = 1.663016837 Solving 0.875 + x = 1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.663016837 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.663016837 + -0.875 x = 1.663016837 + -0.875 Combine like terms: 1.663016837 + -0.875 = 0.788016837 x = 0.788016837 Simplifying x = 0.788016837Subproblem 2
x + 0.875 = -1.663016837 Simplifying x + 0.875 = -1.663016837 Reorder the terms: 0.875 + x = -1.663016837 Solving 0.875 + x = -1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.663016837 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.663016837 + -0.875 x = -1.663016837 + -0.875 Combine like terms: -1.663016837 + -0.875 = -2.538016837 x = -2.538016837 Simplifying x = -2.538016837Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.788016837, -2.538016837}Solution
x = {0, 0.788016837, -2.538016837}
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