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Simplifying a2 + -18a + -63 = 7 Reorder the terms: -63 + -18a + a2 = 7 Solving -63 + -18a + a2 = 7 Solving for variable 'a'. Reorder the terms: -63 + -7 + -18a + a2 = 7 + -7 Combine like terms: -63 + -7 = -70 -70 + -18a + a2 = 7 + -7 Combine like terms: 7 + -7 = 0 -70 + -18a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -18a + 70 + a2 = 0 + 70 Reorder the terms: -70 + 70 + -18a + a2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -18a + a2 = 0 + 70 -18a + a2 = 0 + 70 Combine like terms: 0 + 70 = 70 -18a + a2 = 70 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 = 70 + 81 Reorder the terms: 81 + -18a + a2 = 70 + 81 Combine like terms: 70 + 81 = 151 81 + -18a + a2 = 151 Factor a perfect square on the left side: (a + -9)(a + -9) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (a + -9) equal to 12.288205727 and -12.288205727.Subproblem 1
a + -9 = 12.288205727 Simplifying a + -9 = 12.288205727 Reorder the terms: -9 + a = 12.288205727 Solving -9 + a = 12.288205727 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 = 12.288205727 + 9 Combine like terms: -9 + 9 = 0 0 + a = 12.288205727 + 9 a = 12.288205727 + 9 Combine like terms: 12.288205727 + 9 = 21.288205727 a = 21.288205727 Simplifying a = 21.288205727Subproblem 2
a + -9 = -12.288205727 Simplifying a + -9 = -12.288205727 Reorder the terms: -9 + a = -12.288205727 Solving -9 + a = -12.288205727 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 = -12.288205727 + 9 Combine like terms: -9 + 9 = 0 0 + a = -12.288205727 + 9 a = -12.288205727 + 9 Combine like terms: -12.288205727 + 9 = -3.288205727 a = -3.288205727 Simplifying a = -3.288205727Solution
The solution to the problem is based on the solutions from the subproblems. a = {21.288205727, -3.288205727}
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