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Simplifying 49x2 + 110x + -25 = 0 Reorder the terms: -25 + 110x + 49x2 = 0 Solving -25 + 110x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.5102040816 + 2.244897959x + x2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + 2.244897959x + 0.5102040816 + x2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + 2.244897959x + x2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + 2.244897959x + x2 = 0 + 0.5102040816 2.244897959x + x2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 2.244897959x + x2 = 0.5102040816 The x term is 2.244897959x. Take half its coefficient (1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. 2.244897959x + 1.259891713 + x2 = 0.5102040816 + 1.259891713 Reorder the terms: 1.259891713 + 2.244897959x + x2 = 0.5102040816 + 1.259891713 Combine like terms: 0.5102040816 + 1.259891713 = 1.7700957946 1.259891713 + 2.244897959x + x2 = 1.7700957946 Factor a perfect square on the left side: (x + 1.12244898)(x + 1.12244898) = 1.7700957946 Calculate the square root of the right side: 1.330449471 Break this problem into two subproblems by setting (x + 1.12244898) equal to 1.330449471 and -1.330449471.Subproblem 1
x + 1.12244898 = 1.330449471 Simplifying x + 1.12244898 = 1.330449471 Reorder the terms: 1.12244898 + x = 1.330449471 Solving 1.12244898 + x = 1.330449471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.12244898' to each side of the equation. 1.12244898 + -1.12244898 + x = 1.330449471 + -1.12244898 Combine like terms: 1.12244898 + -1.12244898 = 0.00000000 0.00000000 + x = 1.330449471 + -1.12244898 x = 1.330449471 + -1.12244898 Combine like terms: 1.330449471 + -1.12244898 = 0.208000491 x = 0.208000491 Simplifying x = 0.208000491Subproblem 2
x + 1.12244898 = -1.330449471 Simplifying x + 1.12244898 = -1.330449471 Reorder the terms: 1.12244898 + x = -1.330449471 Solving 1.12244898 + x = -1.330449471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.12244898' to each side of the equation. 1.12244898 + -1.12244898 + x = -1.330449471 + -1.12244898 Combine like terms: 1.12244898 + -1.12244898 = 0.00000000 0.00000000 + x = -1.330449471 + -1.12244898 x = -1.330449471 + -1.12244898 Combine like terms: -1.330449471 + -1.12244898 = -2.452898451 x = -2.452898451 Simplifying x = -2.452898451Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.208000491, -2.452898451}
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