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Simplifying 0 = -32x2 + -16x + -416 Reorder the terms: 0 = -416 + -16x + -32x2 Solving 0 = -416 + -16x + -32x2 Solving for variable 'x'. Combine like terms: 0 + 416 = 416 416 + 16x + 32x2 = -416 + -16x + -32x2 + 416 + 16x + 32x2 Reorder the terms: 416 + 16x + 32x2 = -416 + 416 + -16x + 16x + -32x2 + 32x2 Combine like terms: -416 + 416 = 0 416 + 16x + 32x2 = 0 + -16x + 16x + -32x2 + 32x2 416 + 16x + 32x2 = -16x + 16x + -32x2 + 32x2 Combine like terms: -16x + 16x = 0 416 + 16x + 32x2 = 0 + -32x2 + 32x2 416 + 16x + 32x2 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 416 + 16x + 32x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(26 + x + 2x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(26 + x + 2x2)' equal to zero and attempt to solve: Simplifying 26 + x + 2x2 = 0 Solving 26 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13 + 0.5x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + 0.5x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 0.5x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 0.5x + x2 = 0 + -13 0.5x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 0.5x + x2 = -13 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 = -13 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -13 + 0.25 Combine like terms: -13 + 0.25 = -12.75 0.25 + 0.5x + x2 = -12.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -12.75 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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