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Simplifying 2(2x2 + 13x + 40) = 0 Reorder the terms: 2(40 + 13x + 2x2) = 0 (40 * 2 + 13x * 2 + 2x2 * 2) = 0 (80 + 26x + 4x2) = 0 Solving 80 + 26x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(40 + 13x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying 40 + 13x + 2x2 = 0 Solving 40 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 20 + 6.5x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + 6.5x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 6.5x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 6.5x + x2 = 0 + -20 6.5x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 6.5x + x2 = -20 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -20 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -20 + 10.5625 Combine like terms: -20 + 10.5625 = -9.4375 10.5625 + 6.5x + x2 = -9.4375 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = -9.4375 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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