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Simplifying x2 + -50x = 5 Reorder the terms: -50x + x2 = 5 Solving -50x + x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -50x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -50x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -50x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -50x + x2 = 0 + 5 -50x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -50x + x2 = 5 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 = 5 + 625 Reorder the terms: 625 + -50x + x2 = 5 + 625 Combine like terms: 5 + 625 = 630 625 + -50x + x2 = 630 Factor a perfect square on the left side: (x + -25)(x + -25) = 630 Calculate the square root of the right side: 25.099800796 Break this problem into two subproblems by setting (x + -25) equal to 25.099800796 and -25.099800796.Subproblem 1
x + -25 = 25.099800796 Simplifying x + -25 = 25.099800796 Reorder the terms: -25 + x = 25.099800796 Solving -25 + x = 25.099800796 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 = 25.099800796 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.099800796 + 25 x = 25.099800796 + 25 Combine like terms: 25.099800796 + 25 = 50.099800796 x = 50.099800796 Simplifying x = 50.099800796Subproblem 2
x + -25 = -25.099800796 Simplifying x + -25 = -25.099800796 Reorder the terms: -25 + x = -25.099800796 Solving -25 + x = -25.099800796 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 = -25.099800796 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.099800796 + 25 x = -25.099800796 + 25 Combine like terms: -25.099800796 + 25 = -0.099800796 x = -0.099800796 Simplifying x = -0.099800796Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.099800796, -0.099800796}
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