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Simplifying 17 = 4(a + -2) * 2a Reorder the terms: 17 = 4(-2 + a) * 2a Reorder the terms for easier multiplication: 17 = 4 * 2a(-2 + a) Multiply 4 * 2 17 = 8a(-2 + a) 17 = (-2 * 8a + a * 8a) 17 = (-16a + 8a2) Solving 17 = -16a + 8a2 Solving for variable 'a'. Reorder the terms: 17 + 16a + -8a2 = -16a + 16a + 8a2 + -8a2 Combine like terms: -16a + 16a = 0 17 + 16a + -8a2 = 0 + 8a2 + -8a2 17 + 16a + -8a2 = 8a2 + -8a2 Combine like terms: 8a2 + -8a2 = 0 17 + 16a + -8a2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.125 + -2a + a2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + -2a + 2.125 + a2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + -2a + a2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + -2a + a2 = 0 + 2.125 -2a + a2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 -2a + a2 = 2.125 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 2.125 + 1 Reorder the terms: 1 + -2a + a2 = 2.125 + 1 Combine like terms: 2.125 + 1 = 3.125 1 + -2a + a2 = 3.125 Factor a perfect square on the left side: (a + -1)(a + -1) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (a + -1) equal to 1.767766953 and -1.767766953.Subproblem 1
a + -1 = 1.767766953 Simplifying a + -1 = 1.767766953 Reorder the terms: -1 + a = 1.767766953 Solving -1 + a = 1.767766953 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 1.767766953 + 1 Combine like terms: -1 + 1 = 0 0 + a = 1.767766953 + 1 a = 1.767766953 + 1 Combine like terms: 1.767766953 + 1 = 2.767766953 a = 2.767766953 Simplifying a = 2.767766953Subproblem 2
a + -1 = -1.767766953 Simplifying a + -1 = -1.767766953 Reorder the terms: -1 + a = -1.767766953 Solving -1 + a = -1.767766953 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -1.767766953 + 1 Combine like terms: -1 + 1 = 0 0 + a = -1.767766953 + 1 a = -1.767766953 + 1 Combine like terms: -1.767766953 + 1 = -0.767766953 a = -0.767766953 Simplifying a = -0.767766953Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.767766953, -0.767766953}
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