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Simplifying 4a(1 + -1a) = -36 (1 * 4a + -1a * 4a) = -36 (4a + -4a2) = -36 Solving 4a + -4a2 = -36 Solving for variable 'a'. Reorder the terms: 36 + 4a + -4a2 = -36 + 36 Combine like terms: -36 + 36 = 0 36 + 4a + -4a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + a + -1a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + a + -1a2)' equal to zero and attempt to solve: Simplifying 9 + a + -1a2 = 0 Solving 9 + a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -1a + a2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + -1a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1a + a2 = 0 + 9 -1a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1a + a2 = 9 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. -1a + 0.25 + a2 = 9 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + -1a + a2 = 9.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (a + 0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
a + 0.5 = 3.041381265 Simplifying a + 0.5 = 3.041381265 Reorder the terms: 0.5 + a = 3.041381265 Solving 0.5 + a = 3.041381265 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 3.041381265 + -0.5 a = 3.041381265 + -0.5 Combine like terms: 3.041381265 + -0.5 = 2.541381265 a = 2.541381265 Simplifying a = 2.541381265Subproblem 2
a + 0.5 = -3.041381265 Simplifying a + 0.5 = -3.041381265 Reorder the terms: 0.5 + a = -3.041381265 Solving 0.5 + a = -3.041381265 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -3.041381265 + -0.5 a = -3.041381265 + -0.5 Combine like terms: -3.041381265 + -0.5 = -3.541381265 a = -3.541381265 Simplifying a = -3.541381265Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.541381265, -3.541381265}Solution
a = {2.541381265, -3.541381265}
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