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Simplifying (4x + 5)(x + 2) = 520 Reorder the terms: (5 + 4x)(x + 2) = 520 Reorder the terms: (5 + 4x)(2 + x) = 520 Multiply (5 + 4x) * (2 + x) (5(2 + x) + 4x * (2 + x)) = 520 ((2 * 5 + x * 5) + 4x * (2 + x)) = 520 ((10 + 5x) + 4x * (2 + x)) = 520 (10 + 5x + (2 * 4x + x * 4x)) = 520 (10 + 5x + (8x + 4x2)) = 520 Combine like terms: 5x + 8x = 13x (10 + 13x + 4x2) = 520 Solving 10 + 13x + 4x2 = 520 Solving for variable 'x'. Reorder the terms: 10 + -520 + 13x + 4x2 = 520 + -520 Combine like terms: 10 + -520 = -510 -510 + 13x + 4x2 = 520 + -520 Combine like terms: 520 + -520 = 0 -510 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -127.5 + 3.25x + x2 = 0 Move the constant term to the right: Add '127.5' to each side of the equation. -127.5 + 3.25x + 127.5 + x2 = 0 + 127.5 Reorder the terms: -127.5 + 127.5 + 3.25x + x2 = 0 + 127.5 Combine like terms: -127.5 + 127.5 = 0.0 0.0 + 3.25x + x2 = 0 + 127.5 3.25x + x2 = 0 + 127.5 Combine like terms: 0 + 127.5 = 127.5 3.25x + x2 = 127.5 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 127.5 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 127.5 + 2.640625 Combine like terms: 127.5 + 2.640625 = 130.140625 2.640625 + 3.25x + x2 = 130.140625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 130.140625 Calculate the square root of the right side: 11.407919398 Break this problem into two subproblems by setting (x + 1.625) equal to 11.407919398 and -11.407919398.Subproblem 1
x + 1.625 = 11.407919398 Simplifying x + 1.625 = 11.407919398 Reorder the terms: 1.625 + x = 11.407919398 Solving 1.625 + x = 11.407919398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 11.407919398 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 11.407919398 + -1.625 x = 11.407919398 + -1.625 Combine like terms: 11.407919398 + -1.625 = 9.782919398 x = 9.782919398 Simplifying x = 9.782919398Subproblem 2
x + 1.625 = -11.407919398 Simplifying x + 1.625 = -11.407919398 Reorder the terms: 1.625 + x = -11.407919398 Solving 1.625 + x = -11.407919398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -11.407919398 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -11.407919398 + -1.625 x = -11.407919398 + -1.625 Combine like terms: -11.407919398 + -1.625 = -13.032919398 x = -13.032919398 Simplifying x = -13.032919398Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.782919398, -13.032919398}
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