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Simplifying 17 = 4a(a + -2) + 2a Reorder the terms: 17 = 4a(-2 + a) + 2a 17 = (-2 * 4a + a * 4a) + 2a 17 = (-8a + 4a2) + 2a Reorder the terms: 17 = -8a + 2a + 4a2 Combine like terms: -8a + 2a = -6a 17 = -6a + 4a2 Solving 17 = -6a + 4a2 Solving for variable 'a'. Reorder the terms: 17 + 6a + -4a2 = -6a + 6a + 4a2 + -4a2 Combine like terms: -6a + 6a = 0 17 + 6a + -4a2 = 0 + 4a2 + -4a2 17 + 6a + -4a2 = 4a2 + -4a2 Combine like terms: 4a2 + -4a2 = 0 17 + 6a + -4a2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -4.25 + -1.5a + a2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -1.5a + 4.25 + a2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -1.5a + a2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -1.5a + a2 = 0 + 4.25 -1.5a + a2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -1.5a + a2 = 4.25 The a term is -1.5a. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5a + 0.5625 + a2 = 4.25 + 0.5625 Reorder the terms: 0.5625 + -1.5a + a2 = 4.25 + 0.5625 Combine like terms: 4.25 + 0.5625 = 4.8125 0.5625 + -1.5a + a2 = 4.8125 Factor a perfect square on the left side: (a + -0.75)(a + -0.75) = 4.8125 Calculate the square root of the right side: 2.193741097 Break this problem into two subproblems by setting (a + -0.75) equal to 2.193741097 and -2.193741097.Subproblem 1
a + -0.75 = 2.193741097 Simplifying a + -0.75 = 2.193741097 Reorder the terms: -0.75 + a = 2.193741097 Solving -0.75 + a = 2.193741097 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = 2.193741097 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = 2.193741097 + 0.75 a = 2.193741097 + 0.75 Combine like terms: 2.193741097 + 0.75 = 2.943741097 a = 2.943741097 Simplifying a = 2.943741097Subproblem 2
a + -0.75 = -2.193741097 Simplifying a + -0.75 = -2.193741097 Reorder the terms: -0.75 + a = -2.193741097 Solving -0.75 + a = -2.193741097 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = -2.193741097 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = -2.193741097 + 0.75 a = -2.193741097 + 0.75 Combine like terms: -2.193741097 + 0.75 = -1.443741097 a = -1.443741097 Simplifying a = -1.443741097Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.943741097, -1.443741097}
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