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Simplifying (x + -45) + x(x + -45) + (x + -45) + x = 540 Reorder the terms: (-45 + x) + x(x + -45) + (x + -45) + x = 540 Remove parenthesis around (-45 + x) -45 + x + x(x + -45) + (x + -45) + x = 540 Reorder the terms: -45 + x + x(-45 + x) + (x + -45) + x = 540 -45 + x + (-45 * x + x * x) + (x + -45) + x = 540 -45 + x + (-45x + x2) + (x + -45) + x = 540 Reorder the terms: -45 + x + -45x + x2 + (-45 + x) + x = 540 Remove parenthesis around (-45 + x) -45 + x + -45x + x2 + -45 + x + 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 = -44x -90 + -44x + x + x + x2 = 540 Combine like terms: -44x + x = -43x -90 + -43x + x + x2 = 540 Combine like terms: -43x + x = -42x -90 + -42x + x2 = 540 Solving -90 + -42x + x2 = 540 Solving for variable 'x'. Reorder the terms: -90 + -540 + -42x + x2 = 540 + -540 Combine like terms: -90 + -540 = -630 -630 + -42x + x2 = 540 + -540 Combine like terms: 540 + -540 = 0 -630 + -42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '630' to each side of the equation. -630 + -42x + 630 + x2 = 0 + 630 Reorder the terms: -630 + 630 + -42x + x2 = 0 + 630 Combine like terms: -630 + 630 = 0 0 + -42x + x2 = 0 + 630 -42x + x2 = 0 + 630 Combine like terms: 0 + 630 = 630 -42x + x2 = 630 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = 630 + 441 Reorder the terms: 441 + -42x + x2 = 630 + 441 Combine like terms: 630 + 441 = 1071 441 + -42x + x2 = 1071 Factor a perfect square on the left side: (x + -21)(x + -21) = 1071 Calculate the square root of the right side: 32.726136344 Break this problem into two subproblems by setting (x + -21) equal to 32.726136344 and -32.726136344.Subproblem 1
x + -21 = 32.726136344 Simplifying x + -21 = 32.726136344 Reorder the terms: -21 + x = 32.726136344 Solving -21 + x = 32.726136344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 32.726136344 + 21 Combine like terms: -21 + 21 = 0 0 + x = 32.726136344 + 21 x = 32.726136344 + 21 Combine like terms: 32.726136344 + 21 = 53.726136344 x = 53.726136344 Simplifying x = 53.726136344Subproblem 2
x + -21 = -32.726136344 Simplifying x + -21 = -32.726136344 Reorder the terms: -21 + x = -32.726136344 Solving -21 + x = -32.726136344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -32.726136344 + 21 Combine like terms: -21 + 21 = 0 0 + x = -32.726136344 + 21 x = -32.726136344 + 21 Combine like terms: -32.726136344 + 21 = -11.726136344 x = -11.726136344 Simplifying x = -11.726136344Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.726136344, -11.726136344}
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