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Simplifying a2 + -21a + 56 = 0 Reorder the terms: 56 + -21a + a2 = 0 Solving 56 + -21a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -21a + -56 + a2 = 0 + -56 Reorder the terms: 56 + -56 + -21a + a2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -21a + a2 = 0 + -56 -21a + a2 = 0 + -56 Combine like terms: 0 + -56 = -56 -21a + a2 = -56 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 = -56 + 110.25 Reorder the terms: 110.25 + -21a + a2 = -56 + 110.25 Combine like terms: -56 + 110.25 = 54.25 110.25 + -21a + a2 = 54.25 Factor a perfect square on the left side: (a + -10.5)(a + -10.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (a + -10.5) equal to 7.365459931 and -7.365459931.Subproblem 1
a + -10.5 = 7.365459931 Simplifying a + -10.5 = 7.365459931 Reorder the terms: -10.5 + a = 7.365459931 Solving -10.5 + a = 7.365459931 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 = 7.365459931 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = 7.365459931 + 10.5 a = 7.365459931 + 10.5 Combine like terms: 7.365459931 + 10.5 = 17.865459931 a = 17.865459931 Simplifying a = 17.865459931Subproblem 2
a + -10.5 = -7.365459931 Simplifying a + -10.5 = -7.365459931 Reorder the terms: -10.5 + a = -7.365459931 Solving -10.5 + a = -7.365459931 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 = -7.365459931 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = -7.365459931 + 10.5 a = -7.365459931 + 10.5 Combine like terms: -7.365459931 + 10.5 = 3.134540069 a = 3.134540069 Simplifying a = 3.134540069Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.865459931, 3.134540069}
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