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Simplifying x2 + 40x + -2500 = 0 Reorder the terms: -2500 + 40x + x2 = 0 Solving -2500 + 40x + 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 + 40x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 40x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 40x + x2 = 0 + 2500 40x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 40x + x2 = 2500 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 2500 + 400 Reorder the terms: 400 + 40x + x2 = 2500 + 400 Combine like terms: 2500 + 400 = 2900 400 + 40x + x2 = 2900 Factor a perfect square on the left side: (x + 20)(x + 20) = 2900 Calculate the square root of the right side: 53.851648071 Break this problem into two subproblems by setting (x + 20) equal to 53.851648071 and -53.851648071.Subproblem 1
x + 20 = 53.851648071 Simplifying x + 20 = 53.851648071 Reorder the terms: 20 + x = 53.851648071 Solving 20 + x = 53.851648071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 53.851648071 + -20 Combine like terms: 20 + -20 = 0 0 + x = 53.851648071 + -20 x = 53.851648071 + -20 Combine like terms: 53.851648071 + -20 = 33.851648071 x = 33.851648071 Simplifying x = 33.851648071Subproblem 2
x + 20 = -53.851648071 Simplifying x + 20 = -53.851648071 Reorder the terms: 20 + x = -53.851648071 Solving 20 + x = -53.851648071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -53.851648071 + -20 Combine like terms: 20 + -20 = 0 0 + x = -53.851648071 + -20 x = -53.851648071 + -20 Combine like terms: -53.851648071 + -20 = -73.851648071 x = -73.851648071 Simplifying x = -73.851648071Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.851648071, -73.851648071}
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