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Simplifying 7x2 + -350x + 1124 = 0 Reorder the terms: 1124 + -350x + 7x2 = 0 Solving 1124 + -350x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 160.5714286 + -50x + x2 = 0 Move the constant term to the right: Add '-160.5714286' to each side of the equation. 160.5714286 + -50x + -160.5714286 + x2 = 0 + -160.5714286 Reorder the terms: 160.5714286 + -160.5714286 + -50x + x2 = 0 + -160.5714286 Combine like terms: 160.5714286 + -160.5714286 = 0.0000000 0.0000000 + -50x + x2 = 0 + -160.5714286 -50x + x2 = 0 + -160.5714286 Combine like terms: 0 + -160.5714286 = -160.5714286 -50x + x2 = -160.5714286 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -160.5714286 + 625 Reorder the terms: 625 + -50x + x2 = -160.5714286 + 625 Combine like terms: -160.5714286 + 625 = 464.4285714 625 + -50x + x2 = 464.4285714 Factor a perfect square on the left side: (x + -25)(x + -25) = 464.4285714 Calculate the square root of the right side: 21.550604896 Break this problem into two subproblems by setting (x + -25) equal to 21.550604896 and -21.550604896.Subproblem 1
x + -25 = 21.550604896 Simplifying x + -25 = 21.550604896 Reorder the terms: -25 + x = 21.550604896 Solving -25 + x = 21.550604896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 21.550604896 + 25 Combine like terms: -25 + 25 = 0 0 + x = 21.550604896 + 25 x = 21.550604896 + 25 Combine like terms: 21.550604896 + 25 = 46.550604896 x = 46.550604896 Simplifying x = 46.550604896Subproblem 2
x + -25 = -21.550604896 Simplifying x + -25 = -21.550604896 Reorder the terms: -25 + x = -21.550604896 Solving -25 + x = -21.550604896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -21.550604896 + 25 Combine like terms: -25 + 25 = 0 0 + x = -21.550604896 + 25 x = -21.550604896 + 25 Combine like terms: -21.550604896 + 25 = 3.449395104 x = 3.449395104 Simplifying x = 3.449395104Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.550604896, 3.449395104}
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