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Simplifying a2 + -586.13a + 65936.9 = 0 Reorder the terms: 65936.9 + -586.13a + a2 = 0 Solving 65936.9 + -586.13a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-65936.9' to each side of the equation. 65936.9 + -586.13a + -65936.9 + a2 = 0 + -65936.9 Reorder the terms: 65936.9 + -65936.9 + -586.13a + a2 = 0 + -65936.9 Combine like terms: 65936.9 + -65936.9 = 0.0 0.0 + -586.13a + a2 = 0 + -65936.9 -586.13a + a2 = 0 + -65936.9 Combine like terms: 0 + -65936.9 = -65936.9 -586.13a + a2 = -65936.9 The a term is -586.13a. Take half its coefficient (-293.065). Square it (85887.09423) and add it to both sides. Add '85887.09423' to each side of the equation. -586.13a + 85887.09423 + a2 = -65936.9 + 85887.09423 Reorder the terms: 85887.09423 + -586.13a + a2 = -65936.9 + 85887.09423 Combine like terms: -65936.9 + 85887.09423 = 19950.19423 85887.09423 + -586.13a + a2 = 19950.19423 Factor a perfect square on the left side: (a + -293.065)(a + -293.065) = 19950.19423 Calculate the square root of the right side: 141.245156483 Break this problem into two subproblems by setting (a + -293.065) equal to 141.245156483 and -141.245156483.Subproblem 1
a + -293.065 = 141.245156483 Simplifying a + -293.065 = 141.245156483 Reorder the terms: -293.065 + a = 141.245156483 Solving -293.065 + a = 141.245156483 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '293.065' to each side of the equation. -293.065 + 293.065 + a = 141.245156483 + 293.065 Combine like terms: -293.065 + 293.065 = 0.000 0.000 + a = 141.245156483 + 293.065 a = 141.245156483 + 293.065 Combine like terms: 141.245156483 + 293.065 = 434.310156483 a = 434.310156483 Simplifying a = 434.310156483Subproblem 2
a + -293.065 = -141.245156483 Simplifying a + -293.065 = -141.245156483 Reorder the terms: -293.065 + a = -141.245156483 Solving -293.065 + a = -141.245156483 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '293.065' to each side of the equation. -293.065 + 293.065 + a = -141.245156483 + 293.065 Combine like terms: -293.065 + 293.065 = 0.000 0.000 + a = -141.245156483 + 293.065 a = -141.245156483 + 293.065 Combine like terms: -141.245156483 + 293.065 = 151.819843517 a = 151.819843517 Simplifying a = 151.819843517Solution
The solution to the problem is based on the solutions from the subproblems. a = {434.310156483, 151.819843517}
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