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Simplifying (4x + -3)(4x + -3) = -81 Reorder the terms: (-3 + 4x)(4x + -3) = -81 Reorder the terms: (-3 + 4x)(-3 + 4x) = -81 Multiply (-3 + 4x) * (-3 + 4x) (-3(-3 + 4x) + 4x * (-3 + 4x)) = -81 ((-3 * -3 + 4x * -3) + 4x * (-3 + 4x)) = -81 ((9 + -12x) + 4x * (-3 + 4x)) = -81 (9 + -12x + (-3 * 4x + 4x * 4x)) = -81 (9 + -12x + (-12x + 16x2)) = -81 Combine like terms: -12x + -12x = -24x (9 + -24x + 16x2) = -81 Solving 9 + -24x + 16x2 = -81 Solving for variable 'x'. Reorder the terms: 9 + 81 + -24x + 16x2 = -81 + 81 Combine like terms: 9 + 81 = 90 90 + -24x + 16x2 = -81 + 81 Combine like terms: -81 + 81 = 0 90 + -24x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -12x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -12x + 8x2)' equal to zero and attempt to solve: Simplifying 45 + -12x + 8x2 = 0 Solving 45 + -12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.625 + -1.5x + x2 = 0 Move the constant term to the right: Add '-5.625' to each side of the equation. 5.625 + -1.5x + -5.625 + x2 = 0 + -5.625 Reorder the terms: 5.625 + -5.625 + -1.5x + x2 = 0 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + -1.5x + x2 = 0 + -5.625 -1.5x + x2 = 0 + -5.625 Combine like terms: 0 + -5.625 = -5.625 -1.5x + x2 = -5.625 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -5.625 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -5.625 + 0.5625 Combine like terms: -5.625 + 0.5625 = -5.0625 0.5625 + -1.5x + x2 = -5.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -5.0625 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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