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Simplifying 3x2 + -524x + -37201 = 0 Reorder the terms: -37201 + -524x + 3x2 = 0 Solving -37201 + -524x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12400.33333 + -174.6666667x + x2 = 0 Move the constant term to the right: Add '12400.33333' to each side of the equation. -12400.33333 + -174.6666667x + 12400.33333 + x2 = 0 + 12400.33333 Reorder the terms: -12400.33333 + 12400.33333 + -174.6666667x + x2 = 0 + 12400.33333 Combine like terms: -12400.33333 + 12400.33333 = 0.00000 0.00000 + -174.6666667x + x2 = 0 + 12400.33333 -174.6666667x + x2 = 0 + 12400.33333 Combine like terms: 0 + 12400.33333 = 12400.33333 -174.6666667x + x2 = 12400.33333 The x term is -174.6666667x. Take half its coefficient (-87.33333335). Square it (7627.111114) and add it to both sides. Add '7627.111114' to each side of the equation. -174.6666667x + 7627.111114 + x2 = 12400.33333 + 7627.111114 Reorder the terms: 7627.111114 + -174.6666667x + x2 = 12400.33333 + 7627.111114 Combine like terms: 12400.33333 + 7627.111114 = 20027.444444 7627.111114 + -174.6666667x + x2 = 20027.444444 Factor a perfect square on the left side: (x + -87.33333335)(x + -87.33333335) = 20027.444444 Calculate the square root of the right side: 141.518353735 Break this problem into two subproblems by setting (x + -87.33333335) equal to 141.518353735 and -141.518353735.Subproblem 1
x + -87.33333335 = 141.518353735 Simplifying x + -87.33333335 = 141.518353735 Reorder the terms: -87.33333335 + x = 141.518353735 Solving -87.33333335 + x = 141.518353735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87.33333335' to each side of the equation. -87.33333335 + 87.33333335 + x = 141.518353735 + 87.33333335 Combine like terms: -87.33333335 + 87.33333335 = 0.00000000 0.00000000 + x = 141.518353735 + 87.33333335 x = 141.518353735 + 87.33333335 Combine like terms: 141.518353735 + 87.33333335 = 228.851687085 x = 228.851687085 Simplifying x = 228.851687085Subproblem 2
x + -87.33333335 = -141.518353735 Simplifying x + -87.33333335 = -141.518353735 Reorder the terms: -87.33333335 + x = -141.518353735 Solving -87.33333335 + x = -141.518353735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87.33333335' to each side of the equation. -87.33333335 + 87.33333335 + x = -141.518353735 + 87.33333335 Combine like terms: -87.33333335 + 87.33333335 = 0.00000000 0.00000000 + x = -141.518353735 + 87.33333335 x = -141.518353735 + 87.33333335 Combine like terms: -141.518353735 + 87.33333335 = -54.185020385 x = -54.185020385 Simplifying x = -54.185020385Solution
The solution to the problem is based on the solutions from the subproblems. x = {228.851687085, -54.185020385}
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