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Simplifying 7 + -8x2 = 6x + 16 Reorder the terms: 7 + -8x2 = 16 + 6x Solving 7 + -8x2 = 16 + 6x Solving for variable 'x'. Reorder the terms: 7 + -16 + -6x + -8x2 = 16 + 6x + -16 + -6x Combine like terms: 7 + -16 = -9 -9 + -6x + -8x2 = 16 + 6x + -16 + -6x Reorder the terms: -9 + -6x + -8x2 = 16 + -16 + 6x + -6x Combine like terms: 16 + -16 = 0 -9 + -6x + -8x2 = 0 + 6x + -6x -9 + -6x + -8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -9 + -6x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 6x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 6x + 8x2)' equal to zero and attempt to solve: Simplifying 9 + 6x + 8x2 = 0 Solving 9 + 6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + 0.75x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 0.75x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 0.75x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 0.75x + x2 = 0 + -1.125 0.75x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 0.75x + x2 = -1.125 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -1.125 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -1.125 + 0.140625 Combine like terms: -1.125 + 0.140625 = -0.984375 0.140625 + 0.75x + x2 = -0.984375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -0.984375 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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