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Simplifying -2x2 = x + 18 Reorder the terms: -2x2 = 18 + x Solving -2x2 = 18 + x Solving for variable 'x'. Reorder the terms: -18 + -1x + -2x2 = 18 + x + -18 + -1x Reorder the terms: -18 + -1x + -2x2 = 18 + -18 + x + -1x Combine like terms: 18 + -18 = 0 -18 + -1x + -2x2 = 0 + x + -1x -18 + -1x + -2x2 = x + -1x Combine like terms: x + -1x = 0 -18 + -1x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(18 + x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(18 + x + 2x2)' equal to zero and attempt to solve: Simplifying 18 + x + 2x2 = 0 Solving 18 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9 + 0.5x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 0.5x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 0.5x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 0.5x + x2 = 0 + -9 0.5x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 0.5x + x2 = -9 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = -9 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -9 + 0.25 Combine like terms: -9 + 0.25 = -8.75 0.25 + 0.5x + x2 = -8.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -8.75 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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