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Simplifying 0 = 20x2 + 13x + 15 Reorder the terms: 0 = 15 + 13x + 20x2 Solving 0 = 15 + 13x + 20x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -13x + -20x2 = 15 + 13x + 20x2 + -15 + -13x + -20x2 Reorder the terms: -15 + -13x + -20x2 = 15 + -15 + 13x + -13x + 20x2 + -20x2 Combine like terms: 15 + -15 = 0 -15 + -13x + -20x2 = 0 + 13x + -13x + 20x2 + -20x2 -15 + -13x + -20x2 = 13x + -13x + 20x2 + -20x2 Combine like terms: 13x + -13x = 0 -15 + -13x + -20x2 = 0 + 20x2 + -20x2 -15 + -13x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -15 + -13x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 13x + 20x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 13x + 20x2)' equal to zero and attempt to solve: Simplifying 15 + 13x + 20x2 = 0 Solving 15 + 13x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.75 + 0.65x + x2 = 0.0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.65x + -0.75 + x2 = 0.0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.65x + x2 = 0.0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.65x + x2 = 0.0 + -0.75 0.65x + x2 = 0.0 + -0.75 Combine like terms: 0.0 + -0.75 = -0.75 0.65x + x2 = -0.75 The x term is 0.65x. Take half its coefficient (0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. 0.65x + 0.105625 + x2 = -0.75 + 0.105625 Reorder the terms: 0.105625 + 0.65x + x2 = -0.75 + 0.105625 Combine like terms: -0.75 + 0.105625 = -0.644375 0.105625 + 0.65x + x2 = -0.644375 Factor a perfect square on the left side: (x + 0.325)(x + 0.325) = -0.644375 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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