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Simplifying 0 = 15x2 + 5x + 20 Reorder the terms: 0 = 20 + 5x + 15x2 Solving 0 = 20 + 5x + 15x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -5x + -15x2 = 20 + 5x + 15x2 + -20 + -5x + -15x2 Reorder the terms: -20 + -5x + -15x2 = 20 + -20 + 5x + -5x + 15x2 + -15x2 Combine like terms: 20 + -20 = 0 -20 + -5x + -15x2 = 0 + 5x + -5x + 15x2 + -15x2 -20 + -5x + -15x2 = 5x + -5x + 15x2 + -15x2 Combine like terms: 5x + -5x = 0 -20 + -5x + -15x2 = 0 + 15x2 + -15x2 -20 + -5x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -20 + -5x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(4 + x + 3x2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(4 + x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + x + 3x2 = 0 Solving 4 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.3333333333x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.3333333333x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + -1.333333333 0.3333333333x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.3333333333x + x2 = -1.333333333 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 = -1.333333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -1.333333333 + 0.25 Combine like terms: -1.333333333 + 0.25 = -1.083333333 0.25 + 0.3333333333x + x2 = -1.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.083333333 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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