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Simplifying (8x + 3)(5x + 3) = 594 Reorder the terms: (3 + 8x)(5x + 3) = 594 Reorder the terms: (3 + 8x)(3 + 5x) = 594 Multiply (3 + 8x) * (3 + 5x) (3(3 + 5x) + 8x * (3 + 5x)) = 594 ((3 * 3 + 5x * 3) + 8x * (3 + 5x)) = 594 ((9 + 15x) + 8x * (3 + 5x)) = 594 (9 + 15x + (3 * 8x + 5x * 8x)) = 594 (9 + 15x + (24x + 40x2)) = 594 Combine like terms: 15x + 24x = 39x (9 + 39x + 40x2) = 594 Solving 9 + 39x + 40x2 = 594 Solving for variable 'x'. Reorder the terms: 9 + -594 + 39x + 40x2 = 594 + -594 Combine like terms: 9 + -594 = -585 -585 + 39x + 40x2 = 594 + -594 Combine like terms: 594 + -594 = 0 -585 + 39x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -14.625 + 0.975x + x2 = 0.0 Move the constant term to the right: Add '14.625' to each side of the equation. -14.625 + 0.975x + 14.625 + x2 = 0.0 + 14.625 Reorder the terms: -14.625 + 14.625 + 0.975x + x2 = 0.0 + 14.625 Combine like terms: -14.625 + 14.625 = 0.000 0.000 + 0.975x + x2 = 0.0 + 14.625 0.975x + x2 = 0.0 + 14.625 Combine like terms: 0.0 + 14.625 = 14.625 0.975x + x2 = 14.625 The x term is 0.975x. Take half its coefficient (0.4875). Square it (0.23765625) and add it to both sides. Add '0.23765625' to each side of the equation. 0.975x + 0.23765625 + x2 = 14.625 + 0.23765625 Reorder the terms: 0.23765625 + 0.975x + x2 = 14.625 + 0.23765625 Combine like terms: 14.625 + 0.23765625 = 14.86265625 0.23765625 + 0.975x + x2 = 14.86265625 Factor a perfect square on the left side: (x + 0.4875)(x + 0.4875) = 14.86265625 Calculate the square root of the right side: 3.85521157 Break this problem into two subproblems by setting (x + 0.4875) equal to 3.85521157 and -3.85521157.Subproblem 1
x + 0.4875 = 3.85521157 Simplifying x + 0.4875 = 3.85521157 Reorder the terms: 0.4875 + x = 3.85521157 Solving 0.4875 + x = 3.85521157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4875' to each side of the equation. 0.4875 + -0.4875 + x = 3.85521157 + -0.4875 Combine like terms: 0.4875 + -0.4875 = 0.0000 0.0000 + x = 3.85521157 + -0.4875 x = 3.85521157 + -0.4875 Combine like terms: 3.85521157 + -0.4875 = 3.36771157 x = 3.36771157 Simplifying x = 3.36771157Subproblem 2
x + 0.4875 = -3.85521157 Simplifying x + 0.4875 = -3.85521157 Reorder the terms: 0.4875 + x = -3.85521157 Solving 0.4875 + x = -3.85521157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4875' to each side of the equation. 0.4875 + -0.4875 + x = -3.85521157 + -0.4875 Combine like terms: 0.4875 + -0.4875 = 0.0000 0.0000 + x = -3.85521157 + -0.4875 x = -3.85521157 + -0.4875 Combine like terms: -3.85521157 + -0.4875 = -4.34271157 x = -4.34271157 Simplifying x = -4.34271157Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.36771157, -4.34271157}
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