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Simplifying 0 = 4x2 + 2x + 32 Reorder the terms: 0 = 32 + 2x + 4x2 Solving 0 = 32 + 2x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + -2x + -4x2 = 32 + 2x + 4x2 + -32 + -2x + -4x2 Reorder the terms: -32 + -2x + -4x2 = 32 + -32 + 2x + -2x + 4x2 + -4x2 Combine like terms: 32 + -32 = 0 -32 + -2x + -4x2 = 0 + 2x + -2x + 4x2 + -4x2 -32 + -2x + -4x2 = 2x + -2x + 4x2 + -4x2 Combine like terms: 2x + -2x = 0 -32 + -2x + -4x2 = 0 + 4x2 + -4x2 -32 + -2x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -32 + -2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(16 + x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(16 + x + 2x2)' equal to zero and attempt to solve: Simplifying 16 + x + 2x2 = 0 Solving 16 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8 + 0.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 0.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 0.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 0.5x + x2 = 0 + -8 0.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 0.5x + x2 = -8 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 = -8 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -8 + 0.25 Combine like terms: -8 + 0.25 = -7.75 0.25 + 0.5x + x2 = -7.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -7.75 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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