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Simplifying 2x + -6x2 = 32 Solving 2x + -6x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 2x + -6x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 2x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + x + -3x2)' equal to zero and attempt to solve: Simplifying -16 + x + -3x2 = 0 Solving -16 + x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5.333333333 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -0.3333333333x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -0.3333333333x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -0.3333333333x + x2 = 0 + -5.333333333 -0.3333333333x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -0.3333333333x + x2 = -5.333333333 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. -0.3333333333x + 0.25 + x2 = -5.333333333 + 0.25 Reorder the terms: 0.25 + -0.3333333333x + x2 = -5.333333333 + 0.25 Combine like terms: -5.333333333 + 0.25 = -5.083333333 0.25 + -0.3333333333x + x2 = -5.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -5.083333333 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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