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Simplifying -97 = -5(-7 + -4a) * 2a Reorder the terms for easier multiplication: -97 = -5 * 2a(-7 + -4a) Multiply -5 * 2 -97 = -10a(-7 + -4a) -97 = (-7 * -10a + -4a * -10a) -97 = (70a + 40a2) Solving -97 = 70a + 40a2 Solving for variable 'a'. Reorder the terms: -97 + -70a + -40a2 = 70a + -70a + 40a2 + -40a2 Combine like terms: 70a + -70a = 0 -97 + -70a + -40a2 = 0 + 40a2 + -40a2 -97 + -70a + -40a2 = 40a2 + -40a2 Combine like terms: 40a2 + -40a2 = 0 -97 + -70a + -40a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(97 + 70a + 40a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(97 + 70a + 40a2)' equal to zero and attempt to solve: Simplifying 97 + 70a + 40a2 = 0 Solving 97 + 70a + 40a2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 2.425 + 1.75a + a2 = 0.0 Move the constant term to the right: Add '-2.425' to each side of the equation. 2.425 + 1.75a + -2.425 + a2 = 0.0 + -2.425 Reorder the terms: 2.425 + -2.425 + 1.75a + a2 = 0.0 + -2.425 Combine like terms: 2.425 + -2.425 = 0.000 0.000 + 1.75a + a2 = 0.0 + -2.425 1.75a + a2 = 0.0 + -2.425 Combine like terms: 0.0 + -2.425 = -2.425 1.75a + a2 = -2.425 The a term is 1.75a. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75a + 0.765625 + a2 = -2.425 + 0.765625 Reorder the terms: 0.765625 + 1.75a + a2 = -2.425 + 0.765625 Combine like terms: -2.425 + 0.765625 = -1.659375 0.765625 + 1.75a + a2 = -1.659375 Factor a perfect square on the left side: (a + 0.875)(a + 0.875) = -1.659375 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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