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Simplifying 8(x + -3) = 88 + 4x(5 + 2x) Reorder the terms: 8(-3 + x) = 88 + 4x(5 + 2x) (-3 * 8 + x * 8) = 88 + 4x(5 + 2x) (-24 + 8x) = 88 + 4x(5 + 2x) -24 + 8x = 88 + (5 * 4x + 2x * 4x) -24 + 8x = 88 + (20x + 8x2) Solving -24 + 8x = 88 + 20x + 8x2 Solving for variable 'x'. Reorder the terms: -24 + -88 + 8x + -20x + -8x2 = 88 + 20x + 8x2 + -88 + -20x + -8x2 Combine like terms: -24 + -88 = -112 -112 + 8x + -20x + -8x2 = 88 + 20x + 8x2 + -88 + -20x + -8x2 Combine like terms: 8x + -20x = -12x -112 + -12x + -8x2 = 88 + 20x + 8x2 + -88 + -20x + -8x2 Reorder the terms: -112 + -12x + -8x2 = 88 + -88 + 20x + -20x + 8x2 + -8x2 Combine like terms: 88 + -88 = 0 -112 + -12x + -8x2 = 0 + 20x + -20x + 8x2 + -8x2 -112 + -12x + -8x2 = 20x + -20x + 8x2 + -8x2 Combine like terms: 20x + -20x = 0 -112 + -12x + -8x2 = 0 + 8x2 + -8x2 -112 + -12x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -112 + -12x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(28 + 3x + 2x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(28 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 28 + 3x + 2x2 = 0 Solving 28 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14 + 1.5x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 1.5x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 1.5x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 1.5x + x2 = 0 + -14 1.5x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 1.5x + x2 = -14 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 = -14 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -14 + 0.5625 Combine like terms: -14 + 0.5625 = -13.4375 0.5625 + 1.5x + x2 = -13.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -13.4375 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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