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Simplifying (x + 40)(x + 20) = 600 Reorder the terms: (40 + x)(x + 20) = 600 Reorder the terms: (40 + x)(20 + x) = 600 Multiply (40 + x) * (20 + x) (40(20 + x) + x(20 + x)) = 600 ((20 * 40 + x * 40) + x(20 + x)) = 600 ((800 + 40x) + x(20 + x)) = 600 (800 + 40x + (20 * x + x * x)) = 600 (800 + 40x + (20x + x2)) = 600 Combine like terms: 40x + 20x = 60x (800 + 60x + x2) = 600 Solving 800 + 60x + x2 = 600 Solving for variable 'x'. Reorder the terms: 800 + -600 + 60x + x2 = 600 + -600 Combine like terms: 800 + -600 = 200 200 + 60x + x2 = 600 + -600 Combine like terms: 600 + -600 = 0 200 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + 60x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + 60x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + 60x + x2 = 0 + -200 60x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 60x + x2 = -200 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = -200 + 900 Reorder the terms: 900 + 60x + x2 = -200 + 900 Combine like terms: -200 + 900 = 700 900 + 60x + x2 = 700 Factor a perfect square on the left side: (x + 30)(x + 30) = 700 Calculate the square root of the right side: 26.457513111 Break this problem into two subproblems by setting (x + 30) equal to 26.457513111 and -26.457513111.Subproblem 1
x + 30 = 26.457513111 Simplifying x + 30 = 26.457513111 Reorder the terms: 30 + x = 26.457513111 Solving 30 + x = 26.457513111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 26.457513111 + -30 Combine like terms: 30 + -30 = 0 0 + x = 26.457513111 + -30 x = 26.457513111 + -30 Combine like terms: 26.457513111 + -30 = -3.542486889 x = -3.542486889 Simplifying x = -3.542486889Subproblem 2
x + 30 = -26.457513111 Simplifying x + 30 = -26.457513111 Reorder the terms: 30 + x = -26.457513111 Solving 30 + x = -26.457513111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -26.457513111 + -30 Combine like terms: 30 + -30 = 0 0 + x = -26.457513111 + -30 x = -26.457513111 + -30 Combine like terms: -26.457513111 + -30 = -56.457513111 x = -56.457513111 Simplifying x = -56.457513111Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.542486889, -56.457513111}
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