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Simplifying 0 = 2x2 + 3x + 16 Reorder the terms: 0 = 16 + 3x + 2x2 Solving 0 = 16 + 3x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + -3x + -2x2 = 16 + 3x + 2x2 + -16 + -3x + -2x2 Reorder the terms: -16 + -3x + -2x2 = 16 + -16 + 3x + -3x + 2x2 + -2x2 Combine like terms: 16 + -16 = 0 -16 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2 -16 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 -16 + -3x + -2x2 = 0 + 2x2 + -2x2 -16 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -16 + -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 3x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 16 + 3x + 2x2 = 0 Solving 16 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8 + 1.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 1.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 1.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 1.5x + x2 = 0 + -8 1.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 1.5x + x2 = -8 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -8 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -8 + 0.5625 Combine like terms: -8 + 0.5625 = -7.4375 0.5625 + 1.5x + x2 = -7.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -7.4375 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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