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Simplifying -150x + 2600 + -1x2 = 0 Reorder the terms: 2600 + -150x + -1x2 = 0 Solving 2600 + -150x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2600 + 150x + x2 = 0 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 = 15.691785736 x = 15.691785736 Simplifying x = 15.691785736Subproblem 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 = -165.691785736 x = -165.691785736 Simplifying x = -165.691785736Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.691785736, -165.691785736}
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