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Simplifying -8x2 = 5x + 6 Reorder the terms: -8x2 = 6 + 5x Solving -8x2 = 6 + 5x Solving for variable 'x'. Reorder the terms: -6 + -5x + -8x2 = 6 + 5x + -6 + -5x Reorder the terms: -6 + -5x + -8x2 = 6 + -6 + 5x + -5x Combine like terms: 6 + -6 = 0 -6 + -5x + -8x2 = 0 + 5x + -5x -6 + -5x + -8x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -6 + -5x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 5x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 5x + 8x2)' equal to zero and attempt to solve: Simplifying 6 + 5x + 8x2 = 0 Solving 6 + 5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.75 + 0.625x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.625x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.625x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.625x + x2 = 0 + -0.75 0.625x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.625x + x2 = -0.75 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 = -0.75 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = -0.75 + 0.09765625 Combine like terms: -0.75 + 0.09765625 = -0.65234375 0.09765625 + 0.625x + x2 = -0.65234375 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = -0.65234375 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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