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Simplifying 10a2 + -36a + 160 = 16a + 40 Reorder the terms: 160 + -36a + 10a2 = 16a + 40 Reorder the terms: 160 + -36a + 10a2 = 40 + 16a Solving 160 + -36a + 10a2 = 40 + 16a Solving for variable 'a'. Reorder the terms: 160 + -40 + -36a + -16a + 10a2 = 40 + 16a + -40 + -16a Combine like terms: 160 + -40 = 120 120 + -36a + -16a + 10a2 = 40 + 16a + -40 + -16a Combine like terms: -36a + -16a = -52a 120 + -52a + 10a2 = 40 + 16a + -40 + -16a Reorder the terms: 120 + -52a + 10a2 = 40 + -40 + 16a + -16a Combine like terms: 40 + -40 = 0 120 + -52a + 10a2 = 0 + 16a + -16a 120 + -52a + 10a2 = 16a + -16a Combine like terms: 16a + -16a = 0 120 + -52a + 10a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -26a + 5a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + -26a + 5a2)' equal to zero and attempt to solve: Simplifying 60 + -26a + 5a2 = 0 Solving 60 + -26a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 12 + -5.2a + a2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -5.2a + -12 + a2 = 0 + -12 Reorder the terms: 12 + -12 + -5.2a + a2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5.2a + a2 = 0 + -12 -5.2a + a2 = 0 + -12 Combine like terms: 0 + -12 = -12 -5.2a + a2 = -12 The a term is -5.2a. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2a + 6.76 + a2 = -12 + 6.76 Reorder the terms: 6.76 + -5.2a + a2 = -12 + 6.76 Combine like terms: -12 + 6.76 = -5.24 6.76 + -5.2a + a2 = -5.24 Factor a perfect square on the left side: (a + -2.6)(a + -2.6) = -5.24 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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