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Simplifying a2 + -15a = -42 Reorder the terms: -15a + a2 = -42 Solving -15a + a2 = -42 Solving for variable 'a'. Reorder the terms: 42 + -15a + a2 = -42 + 42 Combine like terms: -42 + 42 = 0 42 + -15a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -15a + -42 + a2 = 0 + -42 Reorder the terms: 42 + -42 + -15a + a2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -15a + a2 = 0 + -42 -15a + a2 = 0 + -42 Combine like terms: 0 + -42 = -42 -15a + a2 = -42 The a term is -15a. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15a + 56.25 + a2 = -42 + 56.25 Reorder the terms: 56.25 + -15a + a2 = -42 + 56.25 Combine like terms: -42 + 56.25 = 14.25 56.25 + -15a + a2 = 14.25 Factor a perfect square on the left side: (a + -7.5)(a + -7.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (a + -7.5) equal to 3.774917218 and -3.774917218.Subproblem 1
a + -7.5 = 3.774917218 Simplifying a + -7.5 = 3.774917218 Reorder the terms: -7.5 + a = 3.774917218 Solving -7.5 + a = 3.774917218 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + a = 3.774917218 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = 3.774917218 + 7.5 a = 3.774917218 + 7.5 Combine like terms: 3.774917218 + 7.5 = 11.274917218 a = 11.274917218 Simplifying a = 11.274917218Subproblem 2
a + -7.5 = -3.774917218 Simplifying a + -7.5 = -3.774917218 Reorder the terms: -7.5 + a = -3.774917218 Solving -7.5 + a = -3.774917218 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + a = -3.774917218 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = -3.774917218 + 7.5 a = -3.774917218 + 7.5 Combine like terms: -3.774917218 + 7.5 = 3.725082782 a = 3.725082782 Simplifying a = 3.725082782Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.274917218, 3.725082782}
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