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Simplifying a2 + 20a + -65 = 6 Reorder the terms: -65 + 20a + a2 = 6 Solving -65 + 20a + a2 = 6 Solving for variable 'a'. Reorder the terms: -65 + -6 + 20a + a2 = 6 + -6 Combine like terms: -65 + -6 = -71 -71 + 20a + a2 = 6 + -6 Combine like terms: 6 + -6 = 0 -71 + 20a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + 20a + 71 + a2 = 0 + 71 Reorder the terms: -71 + 71 + 20a + a2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 20a + a2 = 0 + 71 20a + a2 = 0 + 71 Combine like terms: 0 + 71 = 71 20a + a2 = 71 The a term is 20a. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20a + 100 + a2 = 71 + 100 Reorder the terms: 100 + 20a + a2 = 71 + 100 Combine like terms: 71 + 100 = 171 100 + 20a + a2 = 171 Factor a perfect square on the left side: (a + 10)(a + 10) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (a + 10) equal to 13.076696831 and -13.076696831.Subproblem 1
a + 10 = 13.076696831 Simplifying a + 10 = 13.076696831 Reorder the terms: 10 + a = 13.076696831 Solving 10 + a = 13.076696831 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = 13.076696831 + -10 Combine like terms: 10 + -10 = 0 0 + a = 13.076696831 + -10 a = 13.076696831 + -10 Combine like terms: 13.076696831 + -10 = 3.076696831 a = 3.076696831 Simplifying a = 3.076696831Subproblem 2
a + 10 = -13.076696831 Simplifying a + 10 = -13.076696831 Reorder the terms: 10 + a = -13.076696831 Solving 10 + a = -13.076696831 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = -13.076696831 + -10 Combine like terms: 10 + -10 = 0 0 + a = -13.076696831 + -10 a = -13.076696831 + -10 Combine like terms: -13.076696831 + -10 = -23.076696831 a = -23.076696831 Simplifying a = -23.076696831Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.076696831, -23.076696831}
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