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Simplifying 0 = 5x2 + 15x + 42 Reorder the terms: 0 = 42 + 15x + 5x2 Solving 0 = 42 + 15x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -42 = -42 -42 + -15x + -5x2 = 42 + 15x + 5x2 + -42 + -15x + -5x2 Reorder the terms: -42 + -15x + -5x2 = 42 + -42 + 15x + -15x + 5x2 + -5x2 Combine like terms: 42 + -42 = 0 -42 + -15x + -5x2 = 0 + 15x + -15x + 5x2 + -5x2 -42 + -15x + -5x2 = 15x + -15x + 5x2 + -5x2 Combine like terms: 15x + -15x = 0 -42 + -15x + -5x2 = 0 + 5x2 + -5x2 -42 + -15x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -42 + -15x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(42 + 15x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(42 + 15x + 5x2)' equal to zero and attempt to solve: Simplifying 42 + 15x + 5x2 = 0 Solving 42 + 15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.4 + 3x + x2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + 3x + -8.4 + x2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + 3x + x2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + 3x + x2 = 0 + -8.4 3x + x2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 3x + x2 = -8.4 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -8.4 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -8.4 + 2.25 Combine like terms: -8.4 + 2.25 = -6.15 2.25 + 3x + x2 = -6.15 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -6.15 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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