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Simplifying -5x(x + 2x) = 5(x + 12) Combine like terms: x + 2x = 3x -5x(3x) = 5(x + 12) Remove parenthesis around (3x) -5x * 3x = 5(x + 12) Reorder the terms for easier multiplication: -5 * 3x * x = 5(x + 12) Multiply -5 * 3 -15x * x = 5(x + 12) Multiply x * x -15x2 = 5(x + 12) Reorder the terms: -15x2 = 5(12 + x) -15x2 = (12 * 5 + x * 5) -15x2 = (60 + 5x) Solving -15x2 = 60 + 5x Solving for variable 'x'. Reorder the terms: -60 + -5x + -15x2 = 60 + 5x + -60 + -5x Reorder the terms: -60 + -5x + -15x2 = 60 + -60 + 5x + -5x Combine like terms: 60 + -60 = 0 -60 + -5x + -15x2 = 0 + 5x + -5x -60 + -5x + -15x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -60 + -5x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(12 + x + 3x2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(12 + x + 3x2)' equal to zero and attempt to solve: Simplifying 12 + x + 3x2 = 0 Solving 12 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 0.3333333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 0.3333333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 0.3333333333x + x2 = 0 + -4 0.3333333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 0.3333333333x + x2 = -4 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 = -4 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + 0.3333333333x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 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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