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Simplifying (5x + 3)(5x + 3) = 72x Reorder the terms: (3 + 5x)(5x + 3) = 72x Reorder the terms: (3 + 5x)(3 + 5x) = 72x Multiply (3 + 5x) * (3 + 5x) (3(3 + 5x) + 5x * (3 + 5x)) = 72x ((3 * 3 + 5x * 3) + 5x * (3 + 5x)) = 72x ((9 + 15x) + 5x * (3 + 5x)) = 72x (9 + 15x + (3 * 5x + 5x * 5x)) = 72x (9 + 15x + (15x + 25x2)) = 72x Combine like terms: 15x + 15x = 30x (9 + 30x + 25x2) = 72x Solving 9 + 30x + 25x2 = 72x Solving for variable 'x'. Reorder the terms: 9 + 30x + -72x + 25x2 = 72x + -72x Combine like terms: 30x + -72x = -42x 9 + -42x + 25x2 = 72x + -72x Combine like terms: 72x + -72x = 0 9 + -42x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.36 + -1.68x + x2 = 0 Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + -1.68x + -0.36 + x2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + -1.68x + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + -1.68x + x2 = 0 + -0.36 -1.68x + x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 -1.68x + x2 = -0.36 The x term is -1.68x. Take half its coefficient (-0.84). Square it (0.7056) and add it to both sides. Add '0.7056' to each side of the equation. -1.68x + 0.7056 + x2 = -0.36 + 0.7056 Reorder the terms: 0.7056 + -1.68x + x2 = -0.36 + 0.7056 Combine like terms: -0.36 + 0.7056 = 0.3456 0.7056 + -1.68x + x2 = 0.3456 Factor a perfect square on the left side: (x + -0.84)(x + -0.84) = 0.3456 Calculate the square root of the right side: 0.587877538 Break this problem into two subproblems by setting (x + -0.84) equal to 0.587877538 and -0.587877538.Subproblem 1
x + -0.84 = 0.587877538 Simplifying x + -0.84 = 0.587877538 Reorder the terms: -0.84 + x = 0.587877538 Solving -0.84 + x = 0.587877538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.84' to each side of the equation. -0.84 + 0.84 + x = 0.587877538 + 0.84 Combine like terms: -0.84 + 0.84 = 0.00 0.00 + x = 0.587877538 + 0.84 x = 0.587877538 + 0.84 Combine like terms: 0.587877538 + 0.84 = 1.427877538 x = 1.427877538 Simplifying x = 1.427877538Subproblem 2
x + -0.84 = -0.587877538 Simplifying x + -0.84 = -0.587877538 Reorder the terms: -0.84 + x = -0.587877538 Solving -0.84 + x = -0.587877538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.84' to each side of the equation. -0.84 + 0.84 + x = -0.587877538 + 0.84 Combine like terms: -0.84 + 0.84 = 0.00 0.00 + x = -0.587877538 + 0.84 x = -0.587877538 + 0.84 Combine like terms: -0.587877538 + 0.84 = 0.252122462 x = 0.252122462 Simplifying x = 0.252122462Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.427877538, 0.252122462}
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