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Simplifying (34 + -1x)(21 + -1x) = 600 Multiply (34 + -1x) * (21 + -1x) (34(21 + -1x) + -1x * (21 + -1x)) = 600 ((21 * 34 + -1x * 34) + -1x * (21 + -1x)) = 600 ((714 + -34x) + -1x * (21 + -1x)) = 600 (714 + -34x + (21 * -1x + -1x * -1x)) = 600 (714 + -34x + (-21x + 1x2)) = 600 Combine like terms: -34x + -21x = -55x (714 + -55x + 1x2) = 600 Solving 714 + -55x + 1x2 = 600 Solving for variable 'x'. Reorder the terms: 714 + -600 + -55x + 1x2 = 600 + -600 Combine like terms: 714 + -600 = 114 114 + -55x + 1x2 = 600 + -600 Combine like terms: 600 + -600 = 0 114 + -55x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-114' to each side of the equation. 114 + -55x + -114 + x2 = 0 + -114 Reorder the terms: 114 + -114 + -55x + x2 = 0 + -114 Combine like terms: 114 + -114 = 0 0 + -55x + x2 = 0 + -114 -55x + x2 = 0 + -114 Combine like terms: 0 + -114 = -114 -55x + x2 = -114 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = -114 + 756.25 Reorder the terms: 756.25 + -55x + x2 = -114 + 756.25 Combine like terms: -114 + 756.25 = 642.25 756.25 + -55x + x2 = 642.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 642.25 Calculate the square root of the right side: 25.342651795 Break this problem into two subproblems by setting (x + -27.5) equal to 25.342651795 and -25.342651795.Subproblem 1
x + -27.5 = 25.342651795 Simplifying x + -27.5 = 25.342651795 Reorder the terms: -27.5 + x = 25.342651795 Solving -27.5 + x = 25.342651795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 25.342651795 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 25.342651795 + 27.5 x = 25.342651795 + 27.5 Combine like terms: 25.342651795 + 27.5 = 52.842651795 x = 52.842651795 Simplifying x = 52.842651795Subproblem 2
x + -27.5 = -25.342651795 Simplifying x + -27.5 = -25.342651795 Reorder the terms: -27.5 + x = -25.342651795 Solving -27.5 + x = -25.342651795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -25.342651795 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -25.342651795 + 27.5 x = -25.342651795 + 27.5 Combine like terms: -25.342651795 + 27.5 = 2.157348205 x = 2.157348205 Simplifying x = 2.157348205Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.842651795, 2.157348205}
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