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Simplifying 120x = 500 + x2 Solving 120x = 500 + x2 Solving for variable 'x'. Reorder the terms: -500 + 120x + -1x2 = 500 + x2 + -500 + -1x2 Reorder the terms: -500 + 120x + -1x2 = 500 + -500 + x2 + -1x2 Combine like terms: 500 + -500 = 0 -500 + 120x + -1x2 = 0 + x2 + -1x2 -500 + 120x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -500 + 120x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 500 + -120x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -120x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -120x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -120x + x2 = 0 + -500 -120x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -120x + x2 = -500 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -500 + 3600 Reorder the terms: 3600 + -120x + x2 = -500 + 3600 Combine like terms: -500 + 3600 = 3100 3600 + -120x + x2 = 3100 Factor a perfect square on the left side: (x + -60)(x + -60) = 3100 Calculate the square root of the right side: 55.677643628 Break this problem into two subproblems by setting (x + -60) equal to 55.677643628 and -55.677643628.Subproblem 1
x + -60 = 55.677643628 Simplifying x + -60 = 55.677643628 Reorder the terms: -60 + x = 55.677643628 Solving -60 + x = 55.677643628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 55.677643628 + 60 Combine like terms: -60 + 60 = 0 0 + x = 55.677643628 + 60 x = 55.677643628 + 60 Combine like terms: 55.677643628 + 60 = 115.677643628 x = 115.677643628 Simplifying x = 115.677643628Subproblem 2
x + -60 = -55.677643628 Simplifying x + -60 = -55.677643628 Reorder the terms: -60 + x = -55.677643628 Solving -60 + x = -55.677643628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -55.677643628 + 60 Combine like terms: -60 + 60 = 0 0 + x = -55.677643628 + 60 x = -55.677643628 + 60 Combine like terms: -55.677643628 + 60 = 4.322356372 x = 4.322356372 Simplifying x = 4.322356372Solution
The solution to the problem is based on the solutions from the subproblems. x = {115.677643628, 4.322356372}
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