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Simplifying 0 = 4x2 + -9x + -25 Reorder the terms: 0 = -25 + -9x + 4x2 Solving 0 = -25 + -9x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + 9x + -4x2 = -25 + -9x + 4x2 + 25 + 9x + -4x2 Reorder the terms: 25 + 9x + -4x2 = -25 + 25 + -9x + 9x + 4x2 + -4x2 Combine like terms: -25 + 25 = 0 25 + 9x + -4x2 = 0 + -9x + 9x + 4x2 + -4x2 25 + 9x + -4x2 = -9x + 9x + 4x2 + -4x2 Combine like terms: -9x + 9x = 0 25 + 9x + -4x2 = 0 + 4x2 + -4x2 25 + 9x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 25 + 9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -2.25x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2.25x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2.25x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2.25x + x2 = 0 + 6.25 -2.25x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2.25x + x2 = 6.25 The x term is -2.25x. 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. -2.25x + 1.265625 + x2 = 6.25 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 6.25 + 1.265625 Combine like terms: 6.25 + 1.265625 = 7.515625 1.265625 + -2.25x + x2 = 7.515625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 7.515625 Calculate the square root of the right side: 2.741464025 Break this problem into two subproblems by setting (x + -1.125) equal to 2.741464025 and -2.741464025.Subproblem 1
x + -1.125 = 2.741464025 Simplifying x + -1.125 = 2.741464025 Reorder the terms: -1.125 + x = 2.741464025 Solving -1.125 + x = 2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 2.741464025 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.741464025 + 1.125 x = 2.741464025 + 1.125 Combine like terms: 2.741464025 + 1.125 = 3.866464025 x = 3.866464025 Simplifying x = 3.866464025Subproblem 2
x + -1.125 = -2.741464025 Simplifying x + -1.125 = -2.741464025 Reorder the terms: -1.125 + x = -2.741464025 Solving -1.125 + x = -2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -2.741464025 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.741464025 + 1.125 x = -2.741464025 + 1.125 Combine like terms: -2.741464025 + 1.125 = -1.616464025 x = -1.616464025 Simplifying x = -1.616464025Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.866464025, -1.616464025}
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