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Simplifying x2 + -100x + -2548 = 0 Reorder the terms: -2548 + -100x + x2 = 0 Solving -2548 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2548' to each side of the equation. -2548 + -100x + 2548 + x2 = 0 + 2548 Reorder the terms: -2548 + 2548 + -100x + x2 = 0 + 2548 Combine like terms: -2548 + 2548 = 0 0 + -100x + x2 = 0 + 2548 -100x + x2 = 0 + 2548 Combine like terms: 0 + 2548 = 2548 -100x + x2 = 2548 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 2548 + 2500 Reorder the terms: 2500 + -100x + x2 = 2548 + 2500 Combine like terms: 2548 + 2500 = 5048 2500 + -100x + x2 = 5048 Factor a perfect square on the left side: (x + -50)(x + -50) = 5048 Calculate the square root of the right side: 71.049278673 Break this problem into two subproblems by setting (x + -50) equal to 71.049278673 and -71.049278673.Subproblem 1
x + -50 = 71.049278673 Simplifying x + -50 = 71.049278673 Reorder the terms: -50 + x = 71.049278673 Solving -50 + x = 71.049278673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 71.049278673 + 50 Combine like terms: -50 + 50 = 0 0 + x = 71.049278673 + 50 x = 71.049278673 + 50 Combine like terms: 71.049278673 + 50 = 121.049278673 x = 121.049278673 Simplifying x = 121.049278673Subproblem 2
x + -50 = -71.049278673 Simplifying x + -50 = -71.049278673 Reorder the terms: -50 + x = -71.049278673 Solving -50 + x = -71.049278673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -71.049278673 + 50 Combine like terms: -50 + 50 = 0 0 + x = -71.049278673 + 50 x = -71.049278673 + 50 Combine like terms: -71.049278673 + 50 = -21.049278673 x = -21.049278673 Simplifying x = -21.049278673Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.049278673, -21.049278673}
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