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Simplifying x2 + -208x + -29440 = 0 Reorder the terms: -29440 + -208x + x2 = 0 Solving -29440 + -208x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '29440' to each side of the equation. -29440 + -208x + 29440 + x2 = 0 + 29440 Reorder the terms: -29440 + 29440 + -208x + x2 = 0 + 29440 Combine like terms: -29440 + 29440 = 0 0 + -208x + x2 = 0 + 29440 -208x + x2 = 0 + 29440 Combine like terms: 0 + 29440 = 29440 -208x + x2 = 29440 The x term is -208x. Take half its coefficient (-104). Square it (10816) and add it to both sides. Add '10816' to each side of the equation. -208x + 10816 + x2 = 29440 + 10816 Reorder the terms: 10816 + -208x + x2 = 29440 + 10816 Combine like terms: 29440 + 10816 = 40256 10816 + -208x + x2 = 40256 Factor a perfect square on the left side: (x + -104)(x + -104) = 40256 Calculate the square root of the right side: 200.638979264 Break this problem into two subproblems by setting (x + -104) equal to 200.638979264 and -200.638979264.Subproblem 1
x + -104 = 200.638979264 Simplifying x + -104 = 200.638979264 Reorder the terms: -104 + x = 200.638979264 Solving -104 + x = 200.638979264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '104' to each side of the equation. -104 + 104 + x = 200.638979264 + 104 Combine like terms: -104 + 104 = 0 0 + x = 200.638979264 + 104 x = 200.638979264 + 104 Combine like terms: 200.638979264 + 104 = 304.638979264 x = 304.638979264 Simplifying x = 304.638979264Subproblem 2
x + -104 = -200.638979264 Simplifying x + -104 = -200.638979264 Reorder the terms: -104 + x = -200.638979264 Solving -104 + x = -200.638979264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '104' to each side of the equation. -104 + 104 + x = -200.638979264 + 104 Combine like terms: -104 + 104 = 0 0 + x = -200.638979264 + 104 x = -200.638979264 + 104 Combine like terms: -200.638979264 + 104 = -96.638979264 x = -96.638979264 Simplifying x = -96.638979264Solution
The solution to the problem is based on the solutions from the subproblems. x = {304.638979264, -96.638979264}
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