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Simplifying x2 + -50x = 450 Reorder the terms: -50x + x2 = 450 Solving -50x + x2 = 450 Solving for variable 'x'. Reorder the terms: -450 + -50x + x2 = 450 + -450 Combine like terms: 450 + -450 = 0 -450 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + -50x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + -50x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + -50x + x2 = 0 + 450 -50x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 -50x + x2 = 450 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 = 450 + 625 Reorder the terms: 625 + -50x + x2 = 450 + 625 Combine like terms: 450 + 625 = 1075 625 + -50x + x2 = 1075 Factor a perfect square on the left side: (x + -25)(x + -25) = 1075 Calculate the square root of the right side: 32.787192622 Break this problem into two subproblems by setting (x + -25) equal to 32.787192622 and -32.787192622.Subproblem 1
x + -25 = 32.787192622 Simplifying x + -25 = 32.787192622 Reorder the terms: -25 + x = 32.787192622 Solving -25 + x = 32.787192622 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 = 32.787192622 + 25 Combine like terms: -25 + 25 = 0 0 + x = 32.787192622 + 25 x = 32.787192622 + 25 Combine like terms: 32.787192622 + 25 = 57.787192622 x = 57.787192622 Simplifying x = 57.787192622Subproblem 2
x + -25 = -32.787192622 Simplifying x + -25 = -32.787192622 Reorder the terms: -25 + x = -32.787192622 Solving -25 + x = -32.787192622 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 = -32.787192622 + 25 Combine like terms: -25 + 25 = 0 0 + x = -32.787192622 + 25 x = -32.787192622 + 25 Combine like terms: -32.787192622 + 25 = -7.787192622 x = -7.787192622 Simplifying x = -7.787192622Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.787192622, -7.787192622}
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