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Simplifying a2 + -18a + -37 = 8 Reorder the terms: -37 + -18a + a2 = 8 Solving -37 + -18a + a2 = 8 Solving for variable 'a'. Reorder the terms: -37 + -8 + -18a + a2 = 8 + -8 Combine like terms: -37 + -8 = -45 -45 + -18a + a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -45 + -18a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -18a + 45 + a2 = 0 + 45 Reorder the terms: -45 + 45 + -18a + a2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -18a + a2 = 0 + 45 -18a + a2 = 0 + 45 Combine like terms: 0 + 45 = 45 -18a + a2 = 45 The a term is -18a. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18a + 81 + a2 = 45 + 81 Reorder the terms: 81 + -18a + a2 = 45 + 81 Combine like terms: 45 + 81 = 126 81 + -18a + a2 = 126 Factor a perfect square on the left side: (a + -9)(a + -9) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (a + -9) equal to 11.22497216 and -11.22497216.Subproblem 1
a + -9 = 11.22497216 Simplifying a + -9 = 11.22497216 Reorder the terms: -9 + a = 11.22497216 Solving -9 + a = 11.22497216 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = 11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + a = 11.22497216 + 9 a = 11.22497216 + 9 Combine like terms: 11.22497216 + 9 = 20.22497216 a = 20.22497216 Simplifying a = 20.22497216Subproblem 2
a + -9 = -11.22497216 Simplifying a + -9 = -11.22497216 Reorder the terms: -9 + a = -11.22497216 Solving -9 + a = -11.22497216 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = -11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + a = -11.22497216 + 9 a = -11.22497216 + 9 Combine like terms: -11.22497216 + 9 = -2.22497216 a = -2.22497216 Simplifying a = -2.22497216Solution
The solution to the problem is based on the solutions from the subproblems. a = {20.22497216, -2.22497216}
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