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Simplifying 594 = (x + 7)(x + 4) Reorder the terms: 594 = (7 + x)(x + 4) Reorder the terms: 594 = (7 + x)(4 + x) Multiply (7 + x) * (4 + x) 594 = (7(4 + x) + x(4 + x)) 594 = ((4 * 7 + x * 7) + x(4 + x)) 594 = ((28 + 7x) + x(4 + x)) 594 = (28 + 7x + (4 * x + x * x)) 594 = (28 + 7x + (4x + x2)) Combine like terms: 7x + 4x = 11x 594 = (28 + 11x + x2) Solving 594 = 28 + 11x + x2 Solving for variable 'x'. Combine like terms: 594 + -28 = 566 566 + -11x + -1x2 = 28 + 11x + x2 + -28 + -11x + -1x2 Reorder the terms: 566 + -11x + -1x2 = 28 + -28 + 11x + -11x + x2 + -1x2 Combine like terms: 28 + -28 = 0 566 + -11x + -1x2 = 0 + 11x + -11x + x2 + -1x2 566 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 566 + -11x + -1x2 = 0 + x2 + -1x2 566 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 566 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -566 + 11x + x2 = 0 Move the constant term to the right: Add '566' to each side of the equation. -566 + 11x + 566 + x2 = 0 + 566 Reorder the terms: -566 + 566 + 11x + x2 = 0 + 566 Combine like terms: -566 + 566 = 0 0 + 11x + x2 = 0 + 566 11x + x2 = 0 + 566 Combine like terms: 0 + 566 = 566 11x + x2 = 566 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 566 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 566 + 30.25 Combine like terms: 566 + 30.25 = 596.25 30.25 + 11x + x2 = 596.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 596.25 Calculate the square root of the right side: 24.418230894 Break this problem into two subproblems by setting (x + 5.5) equal to 24.418230894 and -24.418230894.Subproblem 1
x + 5.5 = 24.418230894 Simplifying x + 5.5 = 24.418230894 Reorder the terms: 5.5 + x = 24.418230894 Solving 5.5 + x = 24.418230894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 24.418230894 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 24.418230894 + -5.5 x = 24.418230894 + -5.5 Combine like terms: 24.418230894 + -5.5 = 18.918230894 x = 18.918230894 Simplifying x = 18.918230894Subproblem 2
x + 5.5 = -24.418230894 Simplifying x + 5.5 = -24.418230894 Reorder the terms: 5.5 + x = -24.418230894 Solving 5.5 + x = -24.418230894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -24.418230894 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -24.418230894 + -5.5 x = -24.418230894 + -5.5 Combine like terms: -24.418230894 + -5.5 = -29.918230894 x = -29.918230894 Simplifying x = -29.918230894Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.918230894, -29.918230894}
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