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Simplifying 4x2 + 17x + -12 = 0 Reorder the terms: -12 + 17x + 4x2 = 0 Solving -12 + 17x + 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'. -3 + 4.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4.25x + x2 = 0 + 3 4.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4.25x + x2 = 3 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 3 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 3 + 4.515625 Combine like terms: 3 + 4.515625 = 7.515625 4.515625 + 4.25x + x2 = 7.515625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 7.515625 Calculate the square root of the right side: 2.741464025 Break this problem into two subproblems by setting (x + 2.125) equal to 2.741464025 and -2.741464025.Subproblem 1
x + 2.125 = 2.741464025 Simplifying x + 2.125 = 2.741464025 Reorder the terms: 2.125 + x = 2.741464025 Solving 2.125 + x = 2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 2.741464025 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 2.741464025 + -2.125 x = 2.741464025 + -2.125 Combine like terms: 2.741464025 + -2.125 = 0.616464025 x = 0.616464025 Simplifying x = 0.616464025Subproblem 2
x + 2.125 = -2.741464025 Simplifying x + 2.125 = -2.741464025 Reorder the terms: 2.125 + x = -2.741464025 Solving 2.125 + x = -2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -2.741464025 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -2.741464025 + -2.125 x = -2.741464025 + -2.125 Combine like terms: -2.741464025 + -2.125 = -4.866464025 x = -4.866464025 Simplifying x = -4.866464025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.616464025, -4.866464025}
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