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Simplifying 4x2 + 25x + 9 = 0 Reorder the terms: 9 + 25x + 4x2 = 0 Solving 9 + 25x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 6.25x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 6.25x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 6.25x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 6.25x + x2 = 0 + -2.25 6.25x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 6.25x + x2 = -2.25 The x term is 6.25x. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25x + 9.765625 + x2 = -2.25 + 9.765625 Reorder the terms: 9.765625 + 6.25x + x2 = -2.25 + 9.765625 Combine like terms: -2.25 + 9.765625 = 7.515625 9.765625 + 6.25x + x2 = 7.515625 Factor a perfect square on the left side: (x + 3.125)(x + 3.125) = 7.515625 Calculate the square root of the right side: 2.741464025 Break this problem into two subproblems by setting (x + 3.125) equal to 2.741464025 and -2.741464025.Subproblem 1
x + 3.125 = 2.741464025 Simplifying x + 3.125 = 2.741464025 Reorder the terms: 3.125 + x = 2.741464025 Solving 3.125 + x = 2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = 2.741464025 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 2.741464025 + -3.125 x = 2.741464025 + -3.125 Combine like terms: 2.741464025 + -3.125 = -0.383535975 x = -0.383535975 Simplifying x = -0.383535975Subproblem 2
x + 3.125 = -2.741464025 Simplifying x + 3.125 = -2.741464025 Reorder the terms: 3.125 + x = -2.741464025 Solving 3.125 + x = -2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = -2.741464025 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -2.741464025 + -3.125 x = -2.741464025 + -3.125 Combine like terms: -2.741464025 + -3.125 = -5.866464025 x = -5.866464025 Simplifying x = -5.866464025Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.383535975, -5.866464025}
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