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Simplifying x2 + -50x + 420 = 0 Reorder the terms: 420 + -50x + x2 = 0 Solving 420 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-420' to each side of the equation. 420 + -50x + -420 + x2 = 0 + -420 Reorder the terms: 420 + -420 + -50x + x2 = 0 + -420 Combine like terms: 420 + -420 = 0 0 + -50x + x2 = 0 + -420 -50x + x2 = 0 + -420 Combine like terms: 0 + -420 = -420 -50x + x2 = -420 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 = -420 + 625 Reorder the terms: 625 + -50x + x2 = -420 + 625 Combine like terms: -420 + 625 = 205 625 + -50x + x2 = 205 Factor a perfect square on the left side: (x + -25)(x + -25) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + -25) equal to 14.317821063 and -14.317821063.Subproblem 1
x + -25 = 14.317821063 Simplifying x + -25 = 14.317821063 Reorder the terms: -25 + x = 14.317821063 Solving -25 + x = 14.317821063 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 = 14.317821063 + 25 Combine like terms: -25 + 25 = 0 0 + x = 14.317821063 + 25 x = 14.317821063 + 25 Combine like terms: 14.317821063 + 25 = 39.317821063 x = 39.317821063 Simplifying x = 39.317821063Subproblem 2
x + -25 = -14.317821063 Simplifying x + -25 = -14.317821063 Reorder the terms: -25 + x = -14.317821063 Solving -25 + x = -14.317821063 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 = -14.317821063 + 25 Combine like terms: -25 + 25 = 0 0 + x = -14.317821063 + 25 x = -14.317821063 + 25 Combine like terms: -14.317821063 + 25 = 10.682178937 x = 10.682178937 Simplifying x = 10.682178937Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.317821063, 10.682178937}
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