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Simplifying 4a(5a + 9) = 63 Reorder the terms: 4a(9 + 5a) = 63 (9 * 4a + 5a * 4a) = 63 (36a + 20a2) = 63 Solving 36a + 20a2 = 63 Solving for variable 'a'. Reorder the terms: -63 + 36a + 20a2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 36a + 20a2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -3.15 + 1.8a + a2 = 0.0 Move the constant term to the right: Add '3.15' to each side of the equation. -3.15 + 1.8a + 3.15 + a2 = 0.0 + 3.15 Reorder the terms: -3.15 + 3.15 + 1.8a + a2 = 0.0 + 3.15 Combine like terms: -3.15 + 3.15 = 0.00 0.00 + 1.8a + a2 = 0.0 + 3.15 1.8a + a2 = 0.0 + 3.15 Combine like terms: 0.0 + 3.15 = 3.15 1.8a + a2 = 3.15 The a term is 1.8a. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8a + 0.81 + a2 = 3.15 + 0.81 Reorder the terms: 0.81 + 1.8a + a2 = 3.15 + 0.81 Combine like terms: 3.15 + 0.81 = 3.96 0.81 + 1.8a + a2 = 3.96 Factor a perfect square on the left side: (a + 0.9)(a + 0.9) = 3.96 Calculate the square root of the right side: 1.989974874 Break this problem into two subproblems by setting (a + 0.9) equal to 1.989974874 and -1.989974874.Subproblem 1
a + 0.9 = 1.989974874 Simplifying a + 0.9 = 1.989974874 Reorder the terms: 0.9 + a = 1.989974874 Solving 0.9 + a = 1.989974874 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + a = 1.989974874 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + a = 1.989974874 + -0.9 a = 1.989974874 + -0.9 Combine like terms: 1.989974874 + -0.9 = 1.089974874 a = 1.089974874 Simplifying a = 1.089974874Subproblem 2
a + 0.9 = -1.989974874 Simplifying a + 0.9 = -1.989974874 Reorder the terms: 0.9 + a = -1.989974874 Solving 0.9 + a = -1.989974874 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + a = -1.989974874 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + a = -1.989974874 + -0.9 a = -1.989974874 + -0.9 Combine like terms: -1.989974874 + -0.9 = -2.889974874 a = -2.889974874 Simplifying a = -2.889974874Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.089974874, -2.889974874}
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