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Simplifying x2 + 45x + 350 = 1000 Reorder the terms: 350 + 45x + x2 = 1000 Solving 350 + 45x + x2 = 1000 Solving for variable 'x'. Reorder the terms: 350 + -1000 + 45x + x2 = 1000 + -1000 Combine like terms: 350 + -1000 = -650 -650 + 45x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -650 + 45x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '650' to each side of the equation. -650 + 45x + 650 + x2 = 0 + 650 Reorder the terms: -650 + 650 + 45x + x2 = 0 + 650 Combine like terms: -650 + 650 = 0 0 + 45x + x2 = 0 + 650 45x + x2 = 0 + 650 Combine like terms: 0 + 650 = 650 45x + x2 = 650 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 = 650 + 506.25 Reorder the terms: 506.25 + 45x + x2 = 650 + 506.25 Combine like terms: 650 + 506.25 = 1156.25 506.25 + 45x + x2 = 1156.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 1156.25 Calculate the square root of the right side: 34.003676272 Break this problem into two subproblems by setting (x + 22.5) equal to 34.003676272 and -34.003676272.Subproblem 1
x + 22.5 = 34.003676272 Simplifying x + 22.5 = 34.003676272 Reorder the terms: 22.5 + x = 34.003676272 Solving 22.5 + x = 34.003676272 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 = 34.003676272 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 34.003676272 + -22.5 x = 34.003676272 + -22.5 Combine like terms: 34.003676272 + -22.5 = 11.503676272 x = 11.503676272 Simplifying x = 11.503676272Subproblem 2
x + 22.5 = -34.003676272 Simplifying x + 22.5 = -34.003676272 Reorder the terms: 22.5 + x = -34.003676272 Solving 22.5 + x = -34.003676272 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 = -34.003676272 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -34.003676272 + -22.5 x = -34.003676272 + -22.5 Combine like terms: -34.003676272 + -22.5 = -56.503676272 x = -56.503676272 Simplifying x = -56.503676272Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.503676272, -56.503676272}
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