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Simplifying 4a2 + -8a = 25 Reorder the terms: -8a + 4a2 = 25 Solving -8a + 4a2 = 25 Solving for variable 'a'. Reorder the terms: -25 + -8a + 4a2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -8a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -2a + a2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2a + 6.25 + a2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2a + a2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2a + a2 = 0 + 6.25 -2a + a2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2a + a2 = 6.25 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 6.25 + 1 Reorder the terms: 1 + -2a + a2 = 6.25 + 1 Combine like terms: 6.25 + 1 = 7.25 1 + -2a + a2 = 7.25 Factor a perfect square on the left side: (a + -1)(a + -1) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (a + -1) equal to 2.692582404 and -2.692582404.Subproblem 1
a + -1 = 2.692582404 Simplifying a + -1 = 2.692582404 Reorder the terms: -1 + a = 2.692582404 Solving -1 + a = 2.692582404 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 2.692582404 + 1 Combine like terms: -1 + 1 = 0 0 + a = 2.692582404 + 1 a = 2.692582404 + 1 Combine like terms: 2.692582404 + 1 = 3.692582404 a = 3.692582404 Simplifying a = 3.692582404Subproblem 2
a + -1 = -2.692582404 Simplifying a + -1 = -2.692582404 Reorder the terms: -1 + a = -2.692582404 Solving -1 + a = -2.692582404 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -2.692582404 + 1 Combine like terms: -1 + 1 = 0 0 + a = -2.692582404 + 1 a = -2.692582404 + 1 Combine like terms: -2.692582404 + 1 = -1.692582404 a = -1.692582404 Simplifying a = -1.692582404Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.692582404, -1.692582404}
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