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Simplifying x2 = 50x + 9 Reorder the terms: x2 = 9 + 50x Solving x2 = 9 + 50x Solving for variable 'x'. Reorder the terms: -9 + -50x + x2 = 9 + 50x + -9 + -50x Reorder the terms: -9 + -50x + x2 = 9 + -9 + 50x + -50x Combine like terms: 9 + -9 = 0 -9 + -50x + x2 = 0 + 50x + -50x -9 + -50x + x2 = 50x + -50x Combine like terms: 50x + -50x = 0 -9 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -50x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -50x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -50x + x2 = 0 + 9 -50x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -50x + x2 = 9 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 = 9 + 625 Reorder the terms: 625 + -50x + x2 = 9 + 625 Combine like terms: 9 + 625 = 634 625 + -50x + x2 = 634 Factor a perfect square on the left side: (x + -25)(x + -25) = 634 Calculate the square root of the right side: 25.179356624 Break this problem into two subproblems by setting (x + -25) equal to 25.179356624 and -25.179356624.Subproblem 1
x + -25 = 25.179356624 Simplifying x + -25 = 25.179356624 Reorder the terms: -25 + x = 25.179356624 Solving -25 + x = 25.179356624 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 = 25.179356624 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.179356624 + 25 x = 25.179356624 + 25 Combine like terms: 25.179356624 + 25 = 50.179356624 x = 50.179356624 Simplifying x = 50.179356624Subproblem 2
x + -25 = -25.179356624 Simplifying x + -25 = -25.179356624 Reorder the terms: -25 + x = -25.179356624 Solving -25 + x = -25.179356624 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 = -25.179356624 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.179356624 + 25 x = -25.179356624 + 25 Combine like terms: -25.179356624 + 25 = -0.179356624 x = -0.179356624 Simplifying x = -0.179356624Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.179356624, -0.179356624}
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