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Simplifying x2 + -202x + -79800 = 0 Reorder the terms: -79800 + -202x + x2 = 0 Solving -79800 + -202x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '79800' to each side of the equation. -79800 + -202x + 79800 + x2 = 0 + 79800 Reorder the terms: -79800 + 79800 + -202x + x2 = 0 + 79800 Combine like terms: -79800 + 79800 = 0 0 + -202x + x2 = 0 + 79800 -202x + x2 = 0 + 79800 Combine like terms: 0 + 79800 = 79800 -202x + x2 = 79800 The x term is -202x. Take half its coefficient (-101). Square it (10201) and add it to both sides. Add '10201' to each side of the equation. -202x + 10201 + x2 = 79800 + 10201 Reorder the terms: 10201 + -202x + x2 = 79800 + 10201 Combine like terms: 79800 + 10201 = 90001 10201 + -202x + x2 = 90001 Factor a perfect square on the left side: (x + -101)(x + -101) = 90001 Calculate the square root of the right side: 300.001666662 Break this problem into two subproblems by setting (x + -101) equal to 300.001666662 and -300.001666662.Subproblem 1
x + -101 = 300.001666662 Simplifying x + -101 = 300.001666662 Reorder the terms: -101 + x = 300.001666662 Solving -101 + x = 300.001666662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '101' to each side of the equation. -101 + 101 + x = 300.001666662 + 101 Combine like terms: -101 + 101 = 0 0 + x = 300.001666662 + 101 x = 300.001666662 + 101 Combine like terms: 300.001666662 + 101 = 401.001666662 x = 401.001666662 Simplifying x = 401.001666662Subproblem 2
x + -101 = -300.001666662 Simplifying x + -101 = -300.001666662 Reorder the terms: -101 + x = -300.001666662 Solving -101 + x = -300.001666662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '101' to each side of the equation. -101 + 101 + x = -300.001666662 + 101 Combine like terms: -101 + 101 = 0 0 + x = -300.001666662 + 101 x = -300.001666662 + 101 Combine like terms: -300.001666662 + 101 = -199.001666662 x = -199.001666662 Simplifying x = -199.001666662Solution
The solution to the problem is based on the solutions from the subproblems. x = {401.001666662, -199.001666662}
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