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Simplifying x + x(x + 45) + (x + 45) + (x + 45) = 540 Reorder the terms: x + x(45 + x) + (x + 45) + (x + 45) = 540 x + (45 * x + x * x) + (x + 45) + (x + 45) = 540 x + (45x + x2) + (x + 45) + (x + 45) = 540 Reorder the terms: x + 45x + x2 + (45 + x) + (x + 45) = 540 Remove parenthesis around (45 + x) x + 45x + x2 + 45 + x + (x + 45) = 540 Reorder the terms: x + 45x + x2 + 45 + x + (45 + x) = 540 Remove parenthesis around (45 + x) x + 45x + x2 + 45 + x + 45 + x = 540 Reorder the terms: 45 + 45 + x + 45x + x + x + x2 = 540 Combine like terms: 45 + 45 = 90 90 + x + 45x + x + x + x2 = 540 Combine like terms: x + 45x = 46x 90 + 46x + x + x + x2 = 540 Combine like terms: 46x + x = 47x 90 + 47x + x + x2 = 540 Combine like terms: 47x + x = 48x 90 + 48x + x2 = 540 Solving 90 + 48x + x2 = 540 Solving for variable 'x'. Reorder the terms: 90 + -540 + 48x + x2 = 540 + -540 Combine like terms: 90 + -540 = -450 -450 + 48x + x2 = 540 + -540 Combine like terms: 540 + -540 = 0 -450 + 48x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 48x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 48x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 48x + x2 = 0 + 450 48x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 48x + x2 = 450 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = 450 + 576 Reorder the terms: 576 + 48x + x2 = 450 + 576 Combine like terms: 450 + 576 = 1026 576 + 48x + x2 = 1026 Factor a perfect square on the left side: (x + 24)(x + 24) = 1026 Calculate the square root of the right side: 32.031234756 Break this problem into two subproblems by setting (x + 24) equal to 32.031234756 and -32.031234756.Subproblem 1
x + 24 = 32.031234756 Simplifying x + 24 = 32.031234756 Reorder the terms: 24 + x = 32.031234756 Solving 24 + x = 32.031234756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 32.031234756 + -24 Combine like terms: 24 + -24 = 0 0 + x = 32.031234756 + -24 x = 32.031234756 + -24 Combine like terms: 32.031234756 + -24 = 8.031234756 x = 8.031234756 Simplifying x = 8.031234756Subproblem 2
x + 24 = -32.031234756 Simplifying x + 24 = -32.031234756 Reorder the terms: 24 + x = -32.031234756 Solving 24 + x = -32.031234756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -32.031234756 + -24 Combine like terms: 24 + -24 = 0 0 + x = -32.031234756 + -24 x = -32.031234756 + -24 Combine like terms: -32.031234756 + -24 = -56.031234756 x = -56.031234756 Simplifying x = -56.031234756Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.031234756, -56.031234756}
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