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Simplifying 2a2 + -25a = 80 Reorder the terms: -25a + 2a2 = 80 Solving -25a + 2a2 = 80 Solving for variable 'a'. Reorder the terms: -80 + -25a + 2a2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -25a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40 + -12.5a + a2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -12.5a + 40 + a2 = 0 + 40 Reorder the terms: -40 + 40 + -12.5a + a2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -12.5a + a2 = 0 + 40 -12.5a + a2 = 0 + 40 Combine like terms: 0 + 40 = 40 -12.5a + a2 = 40 The a term is -12.5a. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5a + 39.0625 + a2 = 40 + 39.0625 Reorder the terms: 39.0625 + -12.5a + a2 = 40 + 39.0625 Combine like terms: 40 + 39.0625 = 79.0625 39.0625 + -12.5a + a2 = 79.0625 Factor a perfect square on the left side: (a + -6.25)(a + -6.25) = 79.0625 Calculate the square root of the right side: 8.891709622 Break this problem into two subproblems by setting (a + -6.25) equal to 8.891709622 and -8.891709622.Subproblem 1
a + -6.25 = 8.891709622 Simplifying a + -6.25 = 8.891709622 Reorder the terms: -6.25 + a = 8.891709622 Solving -6.25 + a = 8.891709622 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + a = 8.891709622 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + a = 8.891709622 + 6.25 a = 8.891709622 + 6.25 Combine like terms: 8.891709622 + 6.25 = 15.141709622 a = 15.141709622 Simplifying a = 15.141709622Subproblem 2
a + -6.25 = -8.891709622 Simplifying a + -6.25 = -8.891709622 Reorder the terms: -6.25 + a = -8.891709622 Solving -6.25 + a = -8.891709622 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + a = -8.891709622 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + a = -8.891709622 + 6.25 a = -8.891709622 + 6.25 Combine like terms: -8.891709622 + 6.25 = -2.641709622 a = -2.641709622 Simplifying a = -2.641709622Solution
The solution to the problem is based on the solutions from the subproblems. a = {15.141709622, -2.641709622}
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