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Simplifying 2x2 + 34x + -111 = 0 Reorder the terms: -111 + 34x + 2x2 = 0 Solving -111 + 34x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -55.5 + 17x + x2 = 0 Move the constant term to the right: Add '55.5' to each side of the equation. -55.5 + 17x + 55.5 + x2 = 0 + 55.5 Reorder the terms: -55.5 + 55.5 + 17x + x2 = 0 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + 17x + x2 = 0 + 55.5 17x + x2 = 0 + 55.5 Combine like terms: 0 + 55.5 = 55.5 17x + x2 = 55.5 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 55.5 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 55.5 + 72.25 Combine like terms: 55.5 + 72.25 = 127.75 72.25 + 17x + x2 = 127.75 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 127.75 Calculate the square root of the right side: 11.302654555 Break this problem into two subproblems by setting (x + 8.5) equal to 11.302654555 and -11.302654555.Subproblem 1
x + 8.5 = 11.302654555 Simplifying x + 8.5 = 11.302654555 Reorder the terms: 8.5 + x = 11.302654555 Solving 8.5 + x = 11.302654555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 11.302654555 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 11.302654555 + -8.5 x = 11.302654555 + -8.5 Combine like terms: 11.302654555 + -8.5 = 2.802654555 x = 2.802654555 Simplifying x = 2.802654555Subproblem 2
x + 8.5 = -11.302654555 Simplifying x + 8.5 = -11.302654555 Reorder the terms: 8.5 + x = -11.302654555 Solving 8.5 + x = -11.302654555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -11.302654555 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -11.302654555 + -8.5 x = -11.302654555 + -8.5 Combine like terms: -11.302654555 + -8.5 = -19.802654555 x = -19.802654555 Simplifying x = -19.802654555Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.802654555, -19.802654555}
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