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Simplifying 0 = x2 + 50x + 500 Reorder the terms: 0 = 500 + 50x + x2 Solving 0 = 500 + 50x + x2 Solving for variable 'x'. Combine like terms: 0 + -500 = -500 -500 + -50x + -1x2 = 500 + 50x + x2 + -500 + -50x + -1x2 Reorder the terms: -500 + -50x + -1x2 = 500 + -500 + 50x + -50x + x2 + -1x2 Combine like terms: 500 + -500 = 0 -500 + -50x + -1x2 = 0 + 50x + -50x + x2 + -1x2 -500 + -50x + -1x2 = 50x + -50x + x2 + -1x2 Combine like terms: 50x + -50x = 0 -500 + -50x + -1x2 = 0 + x2 + -1x2 -500 + -50x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -500 + -50x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(500 + 50x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(500 + 50x + x2)' equal to zero and attempt to solve: Simplifying 500 + 50x + x2 = 0 Solving 500 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + 50x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + 50x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + 50x + x2 = 0 + -500 50x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 50x + x2 = -500 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 = -500 + 625 Reorder the terms: 625 + 50x + x2 = -500 + 625 Combine like terms: -500 + 625 = 125 625 + 50x + x2 = 125 Factor a perfect square on the left side: (x + 25)(x + 25) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 25) equal to 11.180339887 and -11.180339887.Subproblem 1
x + 25 = 11.180339887 Simplifying x + 25 = 11.180339887 Reorder the terms: 25 + x = 11.180339887 Solving 25 + x = 11.180339887 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 = 11.180339887 + -25 Combine like terms: 25 + -25 = 0 0 + x = 11.180339887 + -25 x = 11.180339887 + -25 Combine like terms: 11.180339887 + -25 = -13.819660113 x = -13.819660113 Simplifying x = -13.819660113Subproblem 2
x + 25 = -11.180339887 Simplifying x + 25 = -11.180339887 Reorder the terms: 25 + x = -11.180339887 Solving 25 + x = -11.180339887 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 = -11.180339887 + -25 Combine like terms: 25 + -25 = 0 0 + x = -11.180339887 + -25 x = -11.180339887 + -25 Combine like terms: -11.180339887 + -25 = -36.180339887 x = -36.180339887 Simplifying x = -36.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.819660113, -36.180339887}Solution
x = {-13.819660113, -36.180339887}
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