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Simplifying a2 + -900a + 54330.6 = 0 Reorder the terms: 54330.6 + -900a + a2 = 0 Solving 54330.6 + -900a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-54330.6' to each side of the equation. 54330.6 + -900a + -54330.6 + a2 = 0 + -54330.6 Reorder the terms: 54330.6 + -54330.6 + -900a + a2 = 0 + -54330.6 Combine like terms: 54330.6 + -54330.6 = 0.0 0.0 + -900a + a2 = 0 + -54330.6 -900a + a2 = 0 + -54330.6 Combine like terms: 0 + -54330.6 = -54330.6 -900a + a2 = -54330.6 The a term is -900a. Take half its coefficient (-450). Square it (202500) and add it to both sides. Add '202500' to each side of the equation. -900a + 202500 + a2 = -54330.6 + 202500 Reorder the terms: 202500 + -900a + a2 = -54330.6 + 202500 Combine like terms: -54330.6 + 202500 = 148169.4 202500 + -900a + a2 = 148169.4 Factor a perfect square on the left side: (a + -450)(a + -450) = 148169.4 Calculate the square root of the right side: 384.927785435 Break this problem into two subproblems by setting (a + -450) equal to 384.927785435 and -384.927785435.Subproblem 1
a + -450 = 384.927785435 Simplifying a + -450 = 384.927785435 Reorder the terms: -450 + a = 384.927785435 Solving -450 + a = 384.927785435 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + a = 384.927785435 + 450 Combine like terms: -450 + 450 = 0 0 + a = 384.927785435 + 450 a = 384.927785435 + 450 Combine like terms: 384.927785435 + 450 = 834.927785435 a = 834.927785435 Simplifying a = 834.927785435Subproblem 2
a + -450 = -384.927785435 Simplifying a + -450 = -384.927785435 Reorder the terms: -450 + a = -384.927785435 Solving -450 + a = -384.927785435 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + a = -384.927785435 + 450 Combine like terms: -450 + 450 = 0 0 + a = -384.927785435 + 450 a = -384.927785435 + 450 Combine like terms: -384.927785435 + 450 = 65.072214565 a = 65.072214565 Simplifying a = 65.072214565Solution
The solution to the problem is based on the solutions from the subproblems. a = {834.927785435, 65.072214565}
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