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Simplifying a2 + 15a + -800 = 0 Reorder the terms: -800 + 15a + a2 = 0 Solving -800 + 15a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + 15a + 800 + a2 = 0 + 800 Reorder the terms: -800 + 800 + 15a + a2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 15a + a2 = 0 + 800 15a + a2 = 0 + 800 Combine like terms: 0 + 800 = 800 15a + a2 = 800 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 = 800 + 56.25 Reorder the terms: 56.25 + 15a + a2 = 800 + 56.25 Combine like terms: 800 + 56.25 = 856.25 56.25 + 15a + a2 = 856.25 Factor a perfect square on the left side: (a + 7.5)(a + 7.5) = 856.25 Calculate the square root of the right side: 29.261749777 Break this problem into two subproblems by setting (a + 7.5) equal to 29.261749777 and -29.261749777.Subproblem 1
a + 7.5 = 29.261749777 Simplifying a + 7.5 = 29.261749777 Reorder the terms: 7.5 + a = 29.261749777 Solving 7.5 + a = 29.261749777 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 = 29.261749777 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + a = 29.261749777 + -7.5 a = 29.261749777 + -7.5 Combine like terms: 29.261749777 + -7.5 = 21.761749777 a = 21.761749777 Simplifying a = 21.761749777Subproblem 2
a + 7.5 = -29.261749777 Simplifying a + 7.5 = -29.261749777 Reorder the terms: 7.5 + a = -29.261749777 Solving 7.5 + a = -29.261749777 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 = -29.261749777 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + a = -29.261749777 + -7.5 a = -29.261749777 + -7.5 Combine like terms: -29.261749777 + -7.5 = -36.761749777 a = -36.761749777 Simplifying a = -36.761749777Solution
The solution to the problem is based on the solutions from the subproblems. a = {21.761749777, -36.761749777}
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