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Simplifying x2 + 100x + -2500 = 0 Reorder the terms: -2500 + 100x + x2 = 0 Solving -2500 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 100x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 100x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 100x + x2 = 0 + 2500 100x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 100x + x2 = 2500 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 = 2500 + 2500 Reorder the terms: 2500 + 100x + x2 = 2500 + 2500 Combine like terms: 2500 + 2500 = 5000 2500 + 100x + x2 = 5000 Factor a perfect square on the left side: (x + 50)(x + 50) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (x + 50) equal to 70.710678119 and -70.710678119.Subproblem 1
x + 50 = 70.710678119 Simplifying x + 50 = 70.710678119 Reorder the terms: 50 + x = 70.710678119 Solving 50 + x = 70.710678119 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 = 70.710678119 + -50 Combine like terms: 50 + -50 = 0 0 + x = 70.710678119 + -50 x = 70.710678119 + -50 Combine like terms: 70.710678119 + -50 = 20.710678119 x = 20.710678119 Simplifying x = 20.710678119Subproblem 2
x + 50 = -70.710678119 Simplifying x + 50 = -70.710678119 Reorder the terms: 50 + x = -70.710678119 Solving 50 + x = -70.710678119 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 = -70.710678119 + -50 Combine like terms: 50 + -50 = 0 0 + x = -70.710678119 + -50 x = -70.710678119 + -50 Combine like terms: -70.710678119 + -50 = -120.710678119 x = -120.710678119 Simplifying x = -120.710678119Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.710678119, -120.710678119}
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