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Simplifying a2 + 18a + -13 = 0 Reorder the terms: -13 + 18a + a2 = 0 Solving -13 + 18a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 18a + 13 + a2 = 0 + 13 Reorder the terms: -13 + 13 + 18a + a2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 18a + a2 = 0 + 13 18a + a2 = 0 + 13 Combine like terms: 0 + 13 = 13 18a + a2 = 13 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 = 13 + 81 Reorder the terms: 81 + 18a + a2 = 13 + 81 Combine like terms: 13 + 81 = 94 81 + 18a + a2 = 94 Factor a perfect square on the left side: (a + 9)(a + 9) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (a + 9) equal to 9.695359715 and -9.695359715.Subproblem 1
a + 9 = 9.695359715 Simplifying a + 9 = 9.695359715 Reorder the terms: 9 + a = 9.695359715 Solving 9 + a = 9.695359715 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 = 9.695359715 + -9 Combine like terms: 9 + -9 = 0 0 + a = 9.695359715 + -9 a = 9.695359715 + -9 Combine like terms: 9.695359715 + -9 = 0.695359715 a = 0.695359715 Simplifying a = 0.695359715Subproblem 2
a + 9 = -9.695359715 Simplifying a + 9 = -9.695359715 Reorder the terms: 9 + a = -9.695359715 Solving 9 + a = -9.695359715 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 = -9.695359715 + -9 Combine like terms: 9 + -9 = 0 0 + a = -9.695359715 + -9 a = -9.695359715 + -9 Combine like terms: -9.695359715 + -9 = -18.695359715 a = -18.695359715 Simplifying a = -18.695359715Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.695359715, -18.695359715}
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