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Simplifying a2 + 2a + -75 = 0 Reorder the terms: -75 + 2a + a2 = 0 Solving -75 + 2a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 2a + 75 + a2 = 0 + 75 Reorder the terms: -75 + 75 + 2a + a2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 2a + a2 = 0 + 75 2a + a2 = 0 + 75 Combine like terms: 0 + 75 = 75 2a + a2 = 75 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 75 + 1 Reorder the terms: 1 + 2a + a2 = 75 + 1 Combine like terms: 75 + 1 = 76 1 + 2a + a2 = 76 Factor a perfect square on the left side: (a + 1)(a + 1) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (a + 1) equal to 8.717797887 and -8.717797887.Subproblem 1
a + 1 = 8.717797887 Simplifying a + 1 = 8.717797887 Reorder the terms: 1 + a = 8.717797887 Solving 1 + a = 8.717797887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 8.717797887 + -1 Combine like terms: 1 + -1 = 0 0 + a = 8.717797887 + -1 a = 8.717797887 + -1 Combine like terms: 8.717797887 + -1 = 7.717797887 a = 7.717797887 Simplifying a = 7.717797887Subproblem 2
a + 1 = -8.717797887 Simplifying a + 1 = -8.717797887 Reorder the terms: 1 + a = -8.717797887 Solving 1 + a = -8.717797887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -8.717797887 + -1 Combine like terms: 1 + -1 = 0 0 + a = -8.717797887 + -1 a = -8.717797887 + -1 Combine like terms: -8.717797887 + -1 = -9.717797887 a = -9.717797887 Simplifying a = -9.717797887Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.717797887, -9.717797887}
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