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Simplifying 2x2 + 83x + 354 = 0 Reorder the terms: 354 + 83x + 2x2 = 0 Solving 354 + 83x + 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'. 177 + 41.5x + x2 = 0 Move the constant term to the right: Add '-177' to each side of the equation. 177 + 41.5x + -177 + x2 = 0 + -177 Reorder the terms: 177 + -177 + 41.5x + x2 = 0 + -177 Combine like terms: 177 + -177 = 0 0 + 41.5x + x2 = 0 + -177 41.5x + x2 = 0 + -177 Combine like terms: 0 + -177 = -177 41.5x + x2 = -177 The x term is 41.5x. Take half its coefficient (20.75). Square it (430.5625) and add it to both sides. Add '430.5625' to each side of the equation. 41.5x + 430.5625 + x2 = -177 + 430.5625 Reorder the terms: 430.5625 + 41.5x + x2 = -177 + 430.5625 Combine like terms: -177 + 430.5625 = 253.5625 430.5625 + 41.5x + x2 = 253.5625 Factor a perfect square on the left side: (x + 20.75)(x + 20.75) = 253.5625 Calculate the square root of the right side: 15.923645939 Break this problem into two subproblems by setting (x + 20.75) equal to 15.923645939 and -15.923645939.Subproblem 1
x + 20.75 = 15.923645939 Simplifying x + 20.75 = 15.923645939 Reorder the terms: 20.75 + x = 15.923645939 Solving 20.75 + x = 15.923645939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.75' to each side of the equation. 20.75 + -20.75 + x = 15.923645939 + -20.75 Combine like terms: 20.75 + -20.75 = 0.00 0.00 + x = 15.923645939 + -20.75 x = 15.923645939 + -20.75 Combine like terms: 15.923645939 + -20.75 = -4.826354061 x = -4.826354061 Simplifying x = -4.826354061Subproblem 2
x + 20.75 = -15.923645939 Simplifying x + 20.75 = -15.923645939 Reorder the terms: 20.75 + x = -15.923645939 Solving 20.75 + x = -15.923645939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.75' to each side of the equation. 20.75 + -20.75 + x = -15.923645939 + -20.75 Combine like terms: 20.75 + -20.75 = 0.00 0.00 + x = -15.923645939 + -20.75 x = -15.923645939 + -20.75 Combine like terms: -15.923645939 + -20.75 = -36.673645939 x = -36.673645939 Simplifying x = -36.673645939Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.826354061, -36.673645939}
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