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Simplifying 1x2 + 34x + -273 = 0 Reorder the terms: -273 + 34x + 1x2 = 0 Solving -273 + 34x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '273' to each side of the equation. -273 + 34x + 273 + x2 = 0 + 273 Reorder the terms: -273 + 273 + 34x + x2 = 0 + 273 Combine like terms: -273 + 273 = 0 0 + 34x + x2 = 0 + 273 34x + x2 = 0 + 273 Combine like terms: 0 + 273 = 273 34x + x2 = 273 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = 273 + 289 Reorder the terms: 289 + 34x + x2 = 273 + 289 Combine like terms: 273 + 289 = 562 289 + 34x + x2 = 562 Factor a perfect square on the left side: (x + 17)(x + 17) = 562 Calculate the square root of the right side: 23.706539182 Break this problem into two subproblems by setting (x + 17) equal to 23.706539182 and -23.706539182.Subproblem 1
x + 17 = 23.706539182 Simplifying x + 17 = 23.706539182 Reorder the terms: 17 + x = 23.706539182 Solving 17 + x = 23.706539182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 23.706539182 + -17 Combine like terms: 17 + -17 = 0 0 + x = 23.706539182 + -17 x = 23.706539182 + -17 Combine like terms: 23.706539182 + -17 = 6.706539182 x = 6.706539182 Simplifying x = 6.706539182Subproblem 2
x + 17 = -23.706539182 Simplifying x + 17 = -23.706539182 Reorder the terms: 17 + x = -23.706539182 Solving 17 + x = -23.706539182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -23.706539182 + -17 Combine like terms: 17 + -17 = 0 0 + x = -23.706539182 + -17 x = -23.706539182 + -17 Combine like terms: -23.706539182 + -17 = -40.706539182 x = -40.706539182 Simplifying x = -40.706539182Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.706539182, -40.706539182}
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