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Simplifying -3x(2 + 4x) = 60 (2 * -3x + 4x * -3x) = 60 (-6x + -12x2) = 60 Solving -6x + -12x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + -6x + -12x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -6x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-6'. -6(10 + x + 2x2) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(10 + x + 2x2)' equal to zero and attempt to solve: Simplifying 10 + x + 2x2 = 0 Solving 10 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + 0.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 0.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 0.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 0.5x + x2 = 0 + -5 0.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 0.5x + x2 = -5 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 = -5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + 0.5x + x2 = -4.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.75 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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