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Simplifying 4a2 + -1a + -6a + -6 = 0 Reorder the terms: -6 + -1a + -6a + 4a2 = 0 Combine like terms: -1a + -6a = -7a -6 + -7a + 4a2 = 0 Solving -6 + -7a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -1.75a + a2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1.75a + 1.5 + a2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1.75a + a2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.75a + a2 = 0 + 1.5 -1.75a + a2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1.75a + a2 = 1.5 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 = 1.5 + 0.765625 Reorder the terms: 0.765625 + -1.75a + a2 = 1.5 + 0.765625 Combine like terms: 1.5 + 0.765625 = 2.265625 0.765625 + -1.75a + a2 = 2.265625 Factor a perfect square on the left side: (a + -0.875)(a + -0.875) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (a + -0.875) equal to 1.505199322 and -1.505199322.Subproblem 1
a + -0.875 = 1.505199322 Simplifying a + -0.875 = 1.505199322 Reorder the terms: -0.875 + a = 1.505199322 Solving -0.875 + a = 1.505199322 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 = 1.505199322 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + a = 1.505199322 + 0.875 a = 1.505199322 + 0.875 Combine like terms: 1.505199322 + 0.875 = 2.380199322 a = 2.380199322 Simplifying a = 2.380199322Subproblem 2
a + -0.875 = -1.505199322 Simplifying a + -0.875 = -1.505199322 Reorder the terms: -0.875 + a = -1.505199322 Solving -0.875 + a = -1.505199322 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 = -1.505199322 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + a = -1.505199322 + 0.875 a = -1.505199322 + 0.875 Combine like terms: -1.505199322 + 0.875 = -0.630199322 a = -0.630199322 Simplifying a = -0.630199322Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.380199322, -0.630199322}
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