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Simplifying 16x(3x + -3) = -18(x + 10) Reorder the terms: 16x(-3 + 3x) = -18(x + 10) (-3 * 16x + 3x * 16x) = -18(x + 10) (-48x + 48x2) = -18(x + 10) Reorder the terms: -48x + 48x2 = -18(10 + x) -48x + 48x2 = (10 * -18 + x * -18) -48x + 48x2 = (-180 + -18x) Solving -48x + 48x2 = -180 + -18x Solving for variable 'x'. Reorder the terms: 180 + -48x + 18x + 48x2 = -180 + -18x + 180 + 18x Combine like terms: -48x + 18x = -30x 180 + -30x + 48x2 = -180 + -18x + 180 + 18x Reorder the terms: 180 + -30x + 48x2 = -180 + 180 + -18x + 18x Combine like terms: -180 + 180 = 0 180 + -30x + 48x2 = 0 + -18x + 18x 180 + -30x + 48x2 = -18x + 18x Combine like terms: -18x + 18x = 0 180 + -30x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(30 + -5x + 8x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(30 + -5x + 8x2)' equal to zero and attempt to solve: Simplifying 30 + -5x + 8x2 = 0 Solving 30 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.75 + -0.625x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -0.625x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -0.625x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -0.625x + x2 = 0 + -3.75 -0.625x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -0.625x + x2 = -3.75 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 = -3.75 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = -3.75 + 0.09765625 Combine like terms: -3.75 + 0.09765625 = -3.65234375 0.09765625 + -0.625x + x2 = -3.65234375 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = -3.65234375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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