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Simplifying a2 + -21a + -108 = 0 Reorder the terms: -108 + -21a + a2 = 0 Solving -108 + -21a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -21a + 108 + a2 = 0 + 108 Reorder the terms: -108 + 108 + -21a + a2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -21a + a2 = 0 + 108 -21a + a2 = 0 + 108 Combine like terms: 0 + 108 = 108 -21a + a2 = 108 The a term is -21a. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21a + 110.25 + a2 = 108 + 110.25 Reorder the terms: 110.25 + -21a + a2 = 108 + 110.25 Combine like terms: 108 + 110.25 = 218.25 110.25 + -21a + a2 = 218.25 Factor a perfect square on the left side: (a + -10.5)(a + -10.5) = 218.25 Calculate the square root of the right side: 14.773286703 Break this problem into two subproblems by setting (a + -10.5) equal to 14.773286703 and -14.773286703.Subproblem 1
a + -10.5 = 14.773286703 Simplifying a + -10.5 = 14.773286703 Reorder the terms: -10.5 + a = 14.773286703 Solving -10.5 + a = 14.773286703 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = 14.773286703 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = 14.773286703 + 10.5 a = 14.773286703 + 10.5 Combine like terms: 14.773286703 + 10.5 = 25.273286703 a = 25.273286703 Simplifying a = 25.273286703Subproblem 2
a + -10.5 = -14.773286703 Simplifying a + -10.5 = -14.773286703 Reorder the terms: -10.5 + a = -14.773286703 Solving -10.5 + a = -14.773286703 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = -14.773286703 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = -14.773286703 + 10.5 a = -14.773286703 + 10.5 Combine like terms: -14.773286703 + 10.5 = -4.273286703 a = -4.273286703 Simplifying a = -4.273286703Solution
The solution to the problem is based on the solutions from the subproblems. a = {25.273286703, -4.273286703}
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