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Simplifying x2 + 40x + -3600 = 0 Reorder the terms: -3600 + 40x + x2 = 0 Solving -3600 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 40x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 40x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 40x + x2 = 0 + 3600 40x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 40x + x2 = 3600 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 = 3600 + 400 Reorder the terms: 400 + 40x + x2 = 3600 + 400 Combine like terms: 3600 + 400 = 4000 400 + 40x + x2 = 4000 Factor a perfect square on the left side: (x + 20)(x + 20) = 4000 Calculate the square root of the right side: 63.245553203 Break this problem into two subproblems by setting (x + 20) equal to 63.245553203 and -63.245553203.Subproblem 1
x + 20 = 63.245553203 Simplifying x + 20 = 63.245553203 Reorder the terms: 20 + x = 63.245553203 Solving 20 + x = 63.245553203 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 = 63.245553203 + -20 Combine like terms: 20 + -20 = 0 0 + x = 63.245553203 + -20 x = 63.245553203 + -20 Combine like terms: 63.245553203 + -20 = 43.245553203 x = 43.245553203 Simplifying x = 43.245553203Subproblem 2
x + 20 = -63.245553203 Simplifying x + 20 = -63.245553203 Reorder the terms: 20 + x = -63.245553203 Solving 20 + x = -63.245553203 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 = -63.245553203 + -20 Combine like terms: 20 + -20 = 0 0 + x = -63.245553203 + -20 x = -63.245553203 + -20 Combine like terms: -63.245553203 + -20 = -83.245553203 x = -83.245553203 Simplifying x = -83.245553203Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.245553203, -83.245553203}
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