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Simplifying 0 = 2x2 + 4x + 31 Reorder the terms: 0 = 31 + 4x + 2x2 Solving 0 = 31 + 4x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -31 = -31 -31 + -4x + -2x2 = 31 + 4x + 2x2 + -31 + -4x + -2x2 Reorder the terms: -31 + -4x + -2x2 = 31 + -31 + 4x + -4x + 2x2 + -2x2 Combine like terms: 31 + -31 = 0 -31 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 -31 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -31 + -4x + -2x2 = 0 + 2x2 + -2x2 -31 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -31 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(31 + 4x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(31 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying 31 + 4x + 2x2 = 0 Solving 31 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15.5 + 2x + x2 = 0 Move the constant term to the right: Add '-15.5' to each side of the equation. 15.5 + 2x + -15.5 + x2 = 0 + -15.5 Reorder the terms: 15.5 + -15.5 + 2x + x2 = 0 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + 2x + x2 = 0 + -15.5 2x + x2 = 0 + -15.5 Combine like terms: 0 + -15.5 = -15.5 2x + x2 = -15.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -15.5 + 1 Reorder the terms: 1 + 2x + x2 = -15.5 + 1 Combine like terms: -15.5 + 1 = -14.5 1 + 2x + x2 = -14.5 Factor a perfect square on the left side: (x + 1)(x + 1) = -14.5 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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