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Simplifying 4a2 + -9a = 25 Reorder the terms: -9a + 4a2 = 25 Solving -9a + 4a2 = 25 Solving for variable 'a'. Reorder the terms: -25 + -9a + 4a2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -9a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -2.25a + a2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2.25a + 6.25 + a2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2.25a + a2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2.25a + a2 = 0 + 6.25 -2.25a + a2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2.25a + a2 = 6.25 The a term is -2.25a. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25a + 1.265625 + a2 = 6.25 + 1.265625 Reorder the terms: 1.265625 + -2.25a + a2 = 6.25 + 1.265625 Combine like terms: 6.25 + 1.265625 = 7.515625 1.265625 + -2.25a + a2 = 7.515625 Factor a perfect square on the left side: (a + -1.125)(a + -1.125) = 7.515625 Calculate the square root of the right side: 2.741464025 Break this problem into two subproblems by setting (a + -1.125) equal to 2.741464025 and -2.741464025.Subproblem 1
a + -1.125 = 2.741464025 Simplifying a + -1.125 = 2.741464025 Reorder the terms: -1.125 + a = 2.741464025 Solving -1.125 + a = 2.741464025 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + a = 2.741464025 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + a = 2.741464025 + 1.125 a = 2.741464025 + 1.125 Combine like terms: 2.741464025 + 1.125 = 3.866464025 a = 3.866464025 Simplifying a = 3.866464025Subproblem 2
a + -1.125 = -2.741464025 Simplifying a + -1.125 = -2.741464025 Reorder the terms: -1.125 + a = -2.741464025 Solving -1.125 + a = -2.741464025 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + a = -2.741464025 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + a = -2.741464025 + 1.125 a = -2.741464025 + 1.125 Combine like terms: -2.741464025 + 1.125 = -1.616464025 a = -1.616464025 Simplifying a = -1.616464025Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.866464025, -1.616464025}
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