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Simplifying -8(3x + 2) * 6x = 110 Reorder the terms: -8(2 + 3x) * 6x = 110 Reorder the terms for easier multiplication: -8 * 6x(2 + 3x) = 110 Multiply -8 * 6 -48x(2 + 3x) = 110 (2 * -48x + 3x * -48x) = 110 (-96x + -144x2) = 110 Solving -96x + -144x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + -96x + -144x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + -96x + -144x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(55 + 48x + 72x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(55 + 48x + 72x2)' equal to zero and attempt to solve: Simplifying 55 + 48x + 72x2 = 0 Solving 55 + 48x + 72x2 = 0 Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. 0.7638888889 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.7638888889' to each side of the equation. 0.7638888889 + 0.6666666667x + -0.7638888889 + x2 = 0 + -0.7638888889 Reorder the terms: 0.7638888889 + -0.7638888889 + 0.6666666667x + x2 = 0 + -0.7638888889 Combine like terms: 0.7638888889 + -0.7638888889 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + -0.7638888889 0.6666666667x + x2 = 0 + -0.7638888889 Combine like terms: 0 + -0.7638888889 = -0.7638888889 0.6666666667x + x2 = -0.7638888889 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -0.7638888889 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.7638888889 + 0.1111111112 Combine like terms: -0.7638888889 + 0.1111111112 = -0.6527777777 0.1111111112 + 0.6666666667x + x2 = -0.6527777777 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.6527777777 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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