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Simplifying 25x2 + -74x + -49 = 0 Reorder the terms: -49 + -74x + 25x2 = 0 Solving -49 + -74x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.96 + -2.96x + x2 = 0 Move the constant term to the right: Add '1.96' to each side of the equation. -1.96 + -2.96x + 1.96 + x2 = 0 + 1.96 Reorder the terms: -1.96 + 1.96 + -2.96x + x2 = 0 + 1.96 Combine like terms: -1.96 + 1.96 = 0.00 0.00 + -2.96x + x2 = 0 + 1.96 -2.96x + x2 = 0 + 1.96 Combine like terms: 0 + 1.96 = 1.96 -2.96x + x2 = 1.96 The x term is -2.96x. Take half its coefficient (-1.48). Square it (2.1904) and add it to both sides. Add '2.1904' to each side of the equation. -2.96x + 2.1904 + x2 = 1.96 + 2.1904 Reorder the terms: 2.1904 + -2.96x + x2 = 1.96 + 2.1904 Combine like terms: 1.96 + 2.1904 = 4.1504 2.1904 + -2.96x + x2 = 4.1504 Factor a perfect square on the left side: (x + -1.48)(x + -1.48) = 4.1504 Calculate the square root of the right side: 2.037253053 Break this problem into two subproblems by setting (x + -1.48) equal to 2.037253053 and -2.037253053.Subproblem 1
x + -1.48 = 2.037253053 Simplifying x + -1.48 = 2.037253053 Reorder the terms: -1.48 + x = 2.037253053 Solving -1.48 + x = 2.037253053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.48' to each side of the equation. -1.48 + 1.48 + x = 2.037253053 + 1.48 Combine like terms: -1.48 + 1.48 = 0.00 0.00 + x = 2.037253053 + 1.48 x = 2.037253053 + 1.48 Combine like terms: 2.037253053 + 1.48 = 3.517253053 x = 3.517253053 Simplifying x = 3.517253053Subproblem 2
x + -1.48 = -2.037253053 Simplifying x + -1.48 = -2.037253053 Reorder the terms: -1.48 + x = -2.037253053 Solving -1.48 + x = -2.037253053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.48' to each side of the equation. -1.48 + 1.48 + x = -2.037253053 + 1.48 Combine like terms: -1.48 + 1.48 = 0.00 0.00 + x = -2.037253053 + 1.48 x = -2.037253053 + 1.48 Combine like terms: -2.037253053 + 1.48 = -0.557253053 x = -0.557253053 Simplifying x = -0.557253053Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.517253053, -0.557253053}
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