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Simplifying 5(a + -4) * 8a = 55 Reorder the terms: 5(-4 + a) * 8a = 55 Reorder the terms for easier multiplication: 5 * 8a(-4 + a) = 55 Multiply 5 * 8 40a(-4 + a) = 55 (-4 * 40a + a * 40a) = 55 (-160a + 40a2) = 55 Solving -160a + 40a2 = 55 Solving for variable 'a'. Reorder the terms: -55 + -160a + 40a2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -160a + 40a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-11 + -32a + 8a2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-11 + -32a + 8a2)' equal to zero and attempt to solve: Simplifying -11 + -32a + 8a2 = 0 Solving -11 + -32a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + -4a + a2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -4a + 1.375 + a2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -4a + a2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -4a + a2 = 0 + 1.375 -4a + a2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -4a + a2 = 1.375 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 1.375 + 4 Reorder the terms: 4 + -4a + a2 = 1.375 + 4 Combine like terms: 1.375 + 4 = 5.375 4 + -4a + a2 = 5.375 Factor a perfect square on the left side: (a + -2)(a + -2) = 5.375 Calculate the square root of the right side: 2.318404624 Break this problem into two subproblems by setting (a + -2) equal to 2.318404624 and -2.318404624.Subproblem 1
a + -2 = 2.318404624 Simplifying a + -2 = 2.318404624 Reorder the terms: -2 + a = 2.318404624 Solving -2 + a = 2.318404624 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 2.318404624 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.318404624 + 2 a = 2.318404624 + 2 Combine like terms: 2.318404624 + 2 = 4.318404624 a = 4.318404624 Simplifying a = 4.318404624Subproblem 2
a + -2 = -2.318404624 Simplifying a + -2 = -2.318404624 Reorder the terms: -2 + a = -2.318404624 Solving -2 + a = -2.318404624 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -2.318404624 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.318404624 + 2 a = -2.318404624 + 2 Combine like terms: -2.318404624 + 2 = -0.318404624 a = -0.318404624 Simplifying a = -0.318404624Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.318404624, -0.318404624}Solution
a = {4.318404624, -0.318404624}
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