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Simplifying 4900 + -140x + x2 = 2450 Solving 4900 + -140x + x2 = 2450 Solving for variable 'x'. Reorder the terms: 4900 + -2450 + -140x + x2 = 2450 + -2450 Combine like terms: 4900 + -2450 = 2450 2450 + -140x + x2 = 2450 + -2450 Combine like terms: 2450 + -2450 = 0 2450 + -140x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2450' to each side of the equation. 2450 + -140x + -2450 + x2 = 0 + -2450 Reorder the terms: 2450 + -2450 + -140x + x2 = 0 + -2450 Combine like terms: 2450 + -2450 = 0 0 + -140x + x2 = 0 + -2450 -140x + x2 = 0 + -2450 Combine like terms: 0 + -2450 = -2450 -140x + x2 = -2450 The x term is -140x. Take half its coefficient (-70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. -140x + 4900 + x2 = -2450 + 4900 Reorder the terms: 4900 + -140x + x2 = -2450 + 4900 Combine like terms: -2450 + 4900 = 2450 4900 + -140x + x2 = 2450 Factor a perfect square on the left side: (x + -70)(x + -70) = 2450 Calculate the square root of the right side: 49.497474683 Break this problem into two subproblems by setting (x + -70) equal to 49.497474683 and -49.497474683.Subproblem 1
x + -70 = 49.497474683 Simplifying x + -70 = 49.497474683 Reorder the terms: -70 + x = 49.497474683 Solving -70 + x = 49.497474683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = 49.497474683 + 70 Combine like terms: -70 + 70 = 0 0 + x = 49.497474683 + 70 x = 49.497474683 + 70 Combine like terms: 49.497474683 + 70 = 119.497474683 x = 119.497474683 Simplifying x = 119.497474683Subproblem 2
x + -70 = -49.497474683 Simplifying x + -70 = -49.497474683 Reorder the terms: -70 + x = -49.497474683 Solving -70 + x = -49.497474683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = -49.497474683 + 70 Combine like terms: -70 + 70 = 0 0 + x = -49.497474683 + 70 x = -49.497474683 + 70 Combine like terms: -49.497474683 + 70 = 20.502525317 x = 20.502525317 Simplifying x = 20.502525317Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.497474683, 20.502525317}
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