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Simplifying (8x2 + 5x + -6)(-3x) = 0 Reorder the terms: (-6 + 5x + 8x2)(-3x) = 0 Remove parenthesis around (-3x) (-6 + 5x + 8x2) * -3x = 0 Reorder the terms for easier multiplication: -3x(-6 + 5x + 8x2) = 0 (-6 * -3x + 5x * -3x + 8x2 * -3x) = 0 (18x + -15x2 + -24x3) = 0 Solving 18x + -15x2 + -24x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(6 + -5x + -8x2) = 0 Ignore the factor 3.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 '(6 + -5x + -8x2)' equal to zero and attempt to solve: Simplifying 6 + -5x + -8x2 = 0 Solving 6 + -5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.75 + 0.625x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.625x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.625x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.625x + x2 = 0 + 0.75 0.625x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.625x + x2 = 0.75 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 0.75 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 0.75 + 0.09765625 Combine like terms: 0.75 + 0.09765625 = 0.84765625 0.09765625 + 0.625x + x2 = 0.84765625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 0.84765625 Calculate the square root of the right side: 0.920682491 Break this problem into two subproblems by setting (x + 0.3125) equal to 0.920682491 and -0.920682491.Subproblem 1
x + 0.3125 = 0.920682491 Simplifying x + 0.3125 = 0.920682491 Reorder the terms: 0.3125 + x = 0.920682491 Solving 0.3125 + x = 0.920682491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 0.920682491 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 0.920682491 + -0.3125 x = 0.920682491 + -0.3125 Combine like terms: 0.920682491 + -0.3125 = 0.608182491 x = 0.608182491 Simplifying x = 0.608182491Subproblem 2
x + 0.3125 = -0.920682491 Simplifying x + 0.3125 = -0.920682491 Reorder the terms: 0.3125 + x = -0.920682491 Solving 0.3125 + x = -0.920682491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -0.920682491 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -0.920682491 + -0.3125 x = -0.920682491 + -0.3125 Combine like terms: -0.920682491 + -0.3125 = -1.233182491 x = -1.233182491 Simplifying x = -1.233182491Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.608182491, -1.233182491}Solution
x = {0, 0.608182491, -1.233182491}
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