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Simplifying 0 = 8x2 + 10x + 96 Reorder the terms: 0 = 96 + 10x + 8x2 Solving 0 = 96 + 10x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -96 = -96 -96 + -10x + -8x2 = 96 + 10x + 8x2 + -96 + -10x + -8x2 Reorder the terms: -96 + -10x + -8x2 = 96 + -96 + 10x + -10x + 8x2 + -8x2 Combine like terms: 96 + -96 = 0 -96 + -10x + -8x2 = 0 + 10x + -10x + 8x2 + -8x2 -96 + -10x + -8x2 = 10x + -10x + 8x2 + -8x2 Combine like terms: 10x + -10x = 0 -96 + -10x + -8x2 = 0 + 8x2 + -8x2 -96 + -10x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -96 + -10x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(48 + 5x + 4x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(48 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying 48 + 5x + 4x2 = 0 Solving 48 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12 + 1.25x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 1.25x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 1.25x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 1.25x + x2 = 0 + -12 1.25x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 1.25x + x2 = -12 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -12 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -12 + 0.390625 Combine like terms: -12 + 0.390625 = -11.609375 0.390625 + 1.25x + x2 = -11.609375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -11.609375 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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