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Simplifying a2 + -15a + -40 = 0 Reorder the terms: -40 + -15a + a2 = 0 Solving -40 + -15a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -15a + 40 + a2 = 0 + 40 Reorder the terms: -40 + 40 + -15a + a2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -15a + a2 = 0 + 40 -15a + a2 = 0 + 40 Combine like terms: 0 + 40 = 40 -15a + a2 = 40 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 = 40 + 56.25 Reorder the terms: 56.25 + -15a + a2 = 40 + 56.25 Combine like terms: 40 + 56.25 = 96.25 56.25 + -15a + a2 = 96.25 Factor a perfect square on the left side: (a + -7.5)(a + -7.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (a + -7.5) equal to 9.810708435 and -9.810708435.Subproblem 1
a + -7.5 = 9.810708435 Simplifying a + -7.5 = 9.810708435 Reorder the terms: -7.5 + a = 9.810708435 Solving -7.5 + a = 9.810708435 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 = 9.810708435 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = 9.810708435 + 7.5 a = 9.810708435 + 7.5 Combine like terms: 9.810708435 + 7.5 = 17.310708435 a = 17.310708435 Simplifying a = 17.310708435Subproblem 2
a + -7.5 = -9.810708435 Simplifying a + -7.5 = -9.810708435 Reorder the terms: -7.5 + a = -9.810708435 Solving -7.5 + a = -9.810708435 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 = -9.810708435 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = -9.810708435 + 7.5 a = -9.810708435 + 7.5 Combine like terms: -9.810708435 + 7.5 = -2.310708435 a = -2.310708435 Simplifying a = -2.310708435Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.310708435, -2.310708435}
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