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Simplifying a2 + -16a + -66 = 10 Reorder the terms: -66 + -16a + a2 = 10 Solving -66 + -16a + a2 = 10 Solving for variable 'a'. Reorder the terms: -66 + -10 + -16a + a2 = 10 + -10 Combine like terms: -66 + -10 = -76 -76 + -16a + a2 = 10 + -10 Combine like terms: 10 + -10 = 0 -76 + -16a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + -16a + 76 + a2 = 0 + 76 Reorder the terms: -76 + 76 + -16a + a2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + -16a + a2 = 0 + 76 -16a + a2 = 0 + 76 Combine like terms: 0 + 76 = 76 -16a + a2 = 76 The a term is -16a. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16a + 64 + a2 = 76 + 64 Reorder the terms: 64 + -16a + a2 = 76 + 64 Combine like terms: 76 + 64 = 140 64 + -16a + a2 = 140 Factor a perfect square on the left side: (a + -8)(a + -8) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (a + -8) equal to 11.832159566 and -11.832159566.Subproblem 1
a + -8 = 11.832159566 Simplifying a + -8 = 11.832159566 Reorder the terms: -8 + a = 11.832159566 Solving -8 + a = 11.832159566 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = 11.832159566 + 8 Combine like terms: -8 + 8 = 0 0 + a = 11.832159566 + 8 a = 11.832159566 + 8 Combine like terms: 11.832159566 + 8 = 19.832159566 a = 19.832159566 Simplifying a = 19.832159566Subproblem 2
a + -8 = -11.832159566 Simplifying a + -8 = -11.832159566 Reorder the terms: -8 + a = -11.832159566 Solving -8 + a = -11.832159566 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = -11.832159566 + 8 Combine like terms: -8 + 8 = 0 0 + a = -11.832159566 + 8 a = -11.832159566 + 8 Combine like terms: -11.832159566 + 8 = -3.832159566 a = -3.832159566 Simplifying a = -3.832159566Solution
The solution to the problem is based on the solutions from the subproblems. a = {19.832159566, -3.832159566}
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