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Simplifying 75x + -2600 = 225x + -1x2 Reorder the terms: -2600 + 75x = 225x + -1x2 Solving -2600 + 75x = 225x + -1x2 Solving for variable 'x'. Combine like terms: 75x + -225x = -150x -2600 + -150x + x2 = 225x + -1x2 + -225x + x2 Reorder the terms: -2600 + -150x + x2 = 225x + -225x + -1x2 + x2 Combine like terms: 225x + -225x = 0 -2600 + -150x + x2 = 0 + -1x2 + x2 -2600 + -150x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -2600 + -150x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2600' to each side of the equation. -2600 + -150x + 2600 + x2 = 0 + 2600 Reorder the terms: -2600 + 2600 + -150x + x2 = 0 + 2600 Combine like terms: -2600 + 2600 = 0 0 + -150x + x2 = 0 + 2600 -150x + x2 = 0 + 2600 Combine like terms: 0 + 2600 = 2600 -150x + x2 = 2600 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = 2600 + 5625 Reorder the terms: 5625 + -150x + x2 = 2600 + 5625 Combine like terms: 2600 + 5625 = 8225 5625 + -150x + x2 = 8225 Factor a perfect square on the left side: (x + -75)(x + -75) = 8225 Calculate the square root of the right side: 90.691785736 Break this problem into two subproblems by setting (x + -75) equal to 90.691785736 and -90.691785736.Subproblem 1
x + -75 = 90.691785736 Simplifying x + -75 = 90.691785736 Reorder the terms: -75 + x = 90.691785736 Solving -75 + x = 90.691785736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 90.691785736 + 75 Combine like terms: -75 + 75 = 0 0 + x = 90.691785736 + 75 x = 90.691785736 + 75 Combine like terms: 90.691785736 + 75 = 165.691785736 x = 165.691785736 Simplifying x = 165.691785736Subproblem 2
x + -75 = -90.691785736 Simplifying x + -75 = -90.691785736 Reorder the terms: -75 + x = -90.691785736 Solving -75 + x = -90.691785736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -90.691785736 + 75 Combine like terms: -75 + 75 = 0 0 + x = -90.691785736 + 75 x = -90.691785736 + 75 Combine like terms: -90.691785736 + 75 = -15.691785736 x = -15.691785736 Simplifying x = -15.691785736Solution
The solution to the problem is based on the solutions from the subproblems. x = {165.691785736, -15.691785736}
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