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Simplifying a(2a + 5) = 882 Reorder the terms: a(5 + 2a) = 882 (5 * a + 2a * a) = 882 (5a + 2a2) = 882 Solving 5a + 2a2 = 882 Solving for variable 'a'. Reorder the terms: -882 + 5a + 2a2 = 882 + -882 Combine like terms: 882 + -882 = 0 -882 + 5a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -441 + 2.5a + a2 = 0 Move the constant term to the right: Add '441' to each side of the equation. -441 + 2.5a + 441 + a2 = 0 + 441 Reorder the terms: -441 + 441 + 2.5a + a2 = 0 + 441 Combine like terms: -441 + 441 = 0 0 + 2.5a + a2 = 0 + 441 2.5a + a2 = 0 + 441 Combine like terms: 0 + 441 = 441 2.5a + a2 = 441 The a term is 2.5a. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5a + 1.5625 + a2 = 441 + 1.5625 Reorder the terms: 1.5625 + 2.5a + a2 = 441 + 1.5625 Combine like terms: 441 + 1.5625 = 442.5625 1.5625 + 2.5a + a2 = 442.5625 Factor a perfect square on the left side: (a + 1.25)(a + 1.25) = 442.5625 Calculate the square root of the right side: 21.037169486 Break this problem into two subproblems by setting (a + 1.25) equal to 21.037169486 and -21.037169486.Subproblem 1
a + 1.25 = 21.037169486 Simplifying a + 1.25 = 21.037169486 Reorder the terms: 1.25 + a = 21.037169486 Solving 1.25 + a = 21.037169486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + a = 21.037169486 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + a = 21.037169486 + -1.25 a = 21.037169486 + -1.25 Combine like terms: 21.037169486 + -1.25 = 19.787169486 a = 19.787169486 Simplifying a = 19.787169486Subproblem 2
a + 1.25 = -21.037169486 Simplifying a + 1.25 = -21.037169486 Reorder the terms: 1.25 + a = -21.037169486 Solving 1.25 + a = -21.037169486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + a = -21.037169486 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + a = -21.037169486 + -1.25 a = -21.037169486 + -1.25 Combine like terms: -21.037169486 + -1.25 = -22.287169486 a = -22.287169486 Simplifying a = -22.287169486Solution
The solution to the problem is based on the solutions from the subproblems. a = {19.787169486, -22.287169486}
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