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Simplifying 2[a + -4] = 4a[-2a + 4] Reorder the terms: 2[-4 + a] = 4a[-2a + 4] [-4 * 2 + a * 2] = 4a[-2a + 4] [-8 + 2a] = 4a[-2a + 4] Reorder the terms: -8 + 2a = 4a[4 + -2a] -8 + 2a = [4 * 4a + -2a * 4a] -8 + 2a = [16a + -8a2] Solving -8 + 2a = 16a + -8a2 Solving for variable 'a'. Combine like terms: 2a + -16a = -14a -8 + -14a + 8a2 = 16a + -8a2 + -16a + 8a2 Reorder the terms: -8 + -14a + 8a2 = 16a + -16a + -8a2 + 8a2 Combine like terms: 16a + -16a = 0 -8 + -14a + 8a2 = 0 + -8a2 + 8a2 -8 + -14a + 8a2 = -8a2 + 8a2 Combine like terms: -8a2 + 8a2 = 0 -8 + -14a + 8a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -7a + 4a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -7a + 4a2)' equal to zero and attempt to solve: Simplifying -4 + -7a + 4a2 = 0 Solving -4 + -7a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -1.75a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.75a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -1.75a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.75a + a2 = 0 + 1 -1.75a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.75a + a2 = 1 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 = 1 + 0.765625 Reorder the terms: 0.765625 + -1.75a + a2 = 1 + 0.765625 Combine like terms: 1 + 0.765625 = 1.765625 0.765625 + -1.75a + a2 = 1.765625 Factor a perfect square on the left side: (a + -0.875)(a + -0.875) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (a + -0.875) equal to 1.328768227 and -1.328768227.Subproblem 1
a + -0.875 = 1.328768227 Simplifying a + -0.875 = 1.328768227 Reorder the terms: -0.875 + a = 1.328768227 Solving -0.875 + a = 1.328768227 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + a = 1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + a = 1.328768227 + 0.875 a = 1.328768227 + 0.875 Combine like terms: 1.328768227 + 0.875 = 2.203768227 a = 2.203768227 Simplifying a = 2.203768227Subproblem 2
a + -0.875 = -1.328768227 Simplifying a + -0.875 = -1.328768227 Reorder the terms: -0.875 + a = -1.328768227 Solving -0.875 + a = -1.328768227 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + a = -1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + a = -1.328768227 + 0.875 a = -1.328768227 + 0.875 Combine like terms: -1.328768227 + 0.875 = -0.453768227 a = -0.453768227 Simplifying a = -0.453768227Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.203768227, -0.453768227}Solution
a = {2.203768227, -0.453768227}
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