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Simplifying (x2) + 250x + -12600 = 0 x2 + 250x + -12600 = 0 Reorder the terms: -12600 + 250x + x2 = 0 Solving -12600 + 250x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12600' to each side of the equation. -12600 + 250x + 12600 + x2 = 0 + 12600 Reorder the terms: -12600 + 12600 + 250x + x2 = 0 + 12600 Combine like terms: -12600 + 12600 = 0 0 + 250x + x2 = 0 + 12600 250x + x2 = 0 + 12600 Combine like terms: 0 + 12600 = 12600 250x + x2 = 12600 The x term is 250x. Take half its coefficient (125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. 250x + 15625 + x2 = 12600 + 15625 Reorder the terms: 15625 + 250x + x2 = 12600 + 15625 Combine like terms: 12600 + 15625 = 28225 15625 + 250x + x2 = 28225 Factor a perfect square on the left side: (x + 125)(x + 125) = 28225 Calculate the square root of the right side: 168.002976164 Break this problem into two subproblems by setting (x + 125) equal to 168.002976164 and -168.002976164.Subproblem 1
x + 125 = 168.002976164 Simplifying x + 125 = 168.002976164 Reorder the terms: 125 + x = 168.002976164 Solving 125 + x = 168.002976164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = 168.002976164 + -125 Combine like terms: 125 + -125 = 0 0 + x = 168.002976164 + -125 x = 168.002976164 + -125 Combine like terms: 168.002976164 + -125 = 43.002976164 x = 43.002976164 Simplifying x = 43.002976164Subproblem 2
x + 125 = -168.002976164 Simplifying x + 125 = -168.002976164 Reorder the terms: 125 + x = -168.002976164 Solving 125 + x = -168.002976164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = -168.002976164 + -125 Combine like terms: 125 + -125 = 0 0 + x = -168.002976164 + -125 x = -168.002976164 + -125 Combine like terms: -168.002976164 + -125 = -293.002976164 x = -293.002976164 Simplifying x = -293.002976164Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.002976164, -293.002976164}
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