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Simplifying 4a2 + -1a + 5 = 15 Reorder the terms: 5 + -1a + 4a2 = 15 Solving 5 + -1a + 4a2 = 15 Solving for variable 'a'. Reorder the terms: 5 + -15 + -1a + 4a2 = 15 + -15 Combine like terms: 5 + -15 = -10 -10 + -1a + 4a2 = 15 + -15 Combine like terms: 15 + -15 = 0 -10 + -1a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + -0.25a + a2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.25a + 2.5 + a2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.25a + a2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.25a + a2 = 0 + 2.5 -0.25a + a2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.25a + a2 = 2.5 The a term is -0.25a. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25a + 0.015625 + a2 = 2.5 + 0.015625 Reorder the terms: 0.015625 + -0.25a + a2 = 2.5 + 0.015625 Combine like terms: 2.5 + 0.015625 = 2.515625 0.015625 + -0.25a + a2 = 2.515625 Factor a perfect square on the left side: (a + -0.125)(a + -0.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (a + -0.125) equal to 1.586072193 and -1.586072193.Subproblem 1
a + -0.125 = 1.586072193 Simplifying a + -0.125 = 1.586072193 Reorder the terms: -0.125 + a = 1.586072193 Solving -0.125 + a = 1.586072193 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = 1.586072193 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = 1.586072193 + 0.125 a = 1.586072193 + 0.125 Combine like terms: 1.586072193 + 0.125 = 1.711072193 a = 1.711072193 Simplifying a = 1.711072193Subproblem 2
a + -0.125 = -1.586072193 Simplifying a + -0.125 = -1.586072193 Reorder the terms: -0.125 + a = -1.586072193 Solving -0.125 + a = -1.586072193 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = -1.586072193 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = -1.586072193 + 0.125 a = -1.586072193 + 0.125 Combine like terms: -1.586072193 + 0.125 = -1.461072193 a = -1.461072193 Simplifying a = -1.461072193Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.711072193, -1.461072193}
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