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Simplifying 2x(-4x2 + 3x + 64) = 0 Reorder the terms: 2x(64 + 3x + -4x2) = 0 (64 * 2x + 3x * 2x + -4x2 * 2x) = 0 (128x + 6x2 + -8x3) = 0 Solving 128x + 6x2 + -8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(64 + 3x + -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 '(64 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying 64 + 3x + -4x2 = 0 Solving 64 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -16 + -0.75x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -0.75x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -0.75x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -0.75x + x2 = 0 + 16 -0.75x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -0.75x + x2 = 16 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 16 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 16 + 0.140625 Combine like terms: 16 + 0.140625 = 16.140625 0.140625 + -0.75x + x2 = 16.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 16.140625 Calculate the square root of the right side: 4.01753967 Break this problem into two subproblems by setting (x + -0.375) equal to 4.01753967 and -4.01753967.Subproblem 1
x + -0.375 = 4.01753967 Simplifying x + -0.375 = 4.01753967 Reorder the terms: -0.375 + x = 4.01753967 Solving -0.375 + x = 4.01753967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 4.01753967 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 4.01753967 + 0.375 x = 4.01753967 + 0.375 Combine like terms: 4.01753967 + 0.375 = 4.39253967 x = 4.39253967 Simplifying x = 4.39253967Subproblem 2
x + -0.375 = -4.01753967 Simplifying x + -0.375 = -4.01753967 Reorder the terms: -0.375 + x = -4.01753967 Solving -0.375 + x = -4.01753967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -4.01753967 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -4.01753967 + 0.375 x = -4.01753967 + 0.375 Combine like terms: -4.01753967 + 0.375 = -3.64253967 x = -3.64253967 Simplifying x = -3.64253967Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.39253967, -3.64253967}Solution
x = {0, 4.39253967, -3.64253967}
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