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Simplifying x2 + 45x + -20000 = 0 Reorder the terms: -20000 + 45x + x2 = 0 Solving -20000 + 45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20000' to each side of the equation. -20000 + 45x + 20000 + x2 = 0 + 20000 Reorder the terms: -20000 + 20000 + 45x + x2 = 0 + 20000 Combine like terms: -20000 + 20000 = 0 0 + 45x + x2 = 0 + 20000 45x + x2 = 0 + 20000 Combine like terms: 0 + 20000 = 20000 45x + x2 = 20000 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = 20000 + 506.25 Reorder the terms: 506.25 + 45x + x2 = 20000 + 506.25 Combine like terms: 20000 + 506.25 = 20506.25 506.25 + 45x + x2 = 20506.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 20506.25 Calculate the square root of the right side: 143.200034916 Break this problem into two subproblems by setting (x + 22.5) equal to 143.200034916 and -143.200034916.Subproblem 1
x + 22.5 = 143.200034916 Simplifying x + 22.5 = 143.200034916 Reorder the terms: 22.5 + x = 143.200034916 Solving 22.5 + x = 143.200034916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 143.200034916 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 143.200034916 + -22.5 x = 143.200034916 + -22.5 Combine like terms: 143.200034916 + -22.5 = 120.700034916 x = 120.700034916 Simplifying x = 120.700034916Subproblem 2
x + 22.5 = -143.200034916 Simplifying x + 22.5 = -143.200034916 Reorder the terms: 22.5 + x = -143.200034916 Solving 22.5 + x = -143.200034916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -143.200034916 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -143.200034916 + -22.5 x = -143.200034916 + -22.5 Combine like terms: -143.200034916 + -22.5 = -165.700034916 x = -165.700034916 Simplifying x = -165.700034916Solution
The solution to the problem is based on the solutions from the subproblems. x = {120.700034916, -165.700034916}
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