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Simplifying -4a * 2a * 1 + -5a + -6a = 10 + -10a Reorder the terms for easier multiplication: -4 * 2 * 1a * a + -5a + -6a = 10 + -10a Multiply -4 * 2 -8 * 1a * a + -5a + -6a = 10 + -10a Multiply -8 * 1 -8a * a + -5a + -6a = 10 + -10a Multiply a * a -8a2 + -5a + -6a = 10 + -10a Reorder the terms: -5a + -6a + -8a2 = 10 + -10a Combine like terms: -5a + -6a = -11a -11a + -8a2 = 10 + -10a Solving -11a + -8a2 = 10 + -10a Solving for variable 'a'. Reorder the terms: -10 + -11a + 10a + -8a2 = 10 + -10a + -10 + 10a Combine like terms: -11a + 10a = -1a -10 + -1a + -8a2 = 10 + -10a + -10 + 10a Reorder the terms: -10 + -1a + -8a2 = 10 + -10 + -10a + 10a Combine like terms: 10 + -10 = 0 -10 + -1a + -8a2 = 0 + -10a + 10a -10 + -1a + -8a2 = -10a + 10a Combine like terms: -10a + 10a = 0 -10 + -1a + -8a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + a + 8a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + a + 8a2)' equal to zero and attempt to solve: Simplifying 10 + a + 8a2 = 0 Solving 10 + a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.25 + 0.125a + a2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.125a + -1.25 + a2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.125a + a2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.125a + a2 = 0 + -1.25 0.125a + a2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.125a + a2 = -1.25 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125a + 0.25 + a2 = -1.25 + 0.25 Reorder the terms: 0.25 + 0.125a + a2 = -1.25 + 0.25 Combine like terms: -1.25 + 0.25 = -1 0.25 + 0.125a + a2 = -1 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -1 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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