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Simplifying (4x + 3)(4x + 3) = 72 Reorder the terms: (3 + 4x)(4x + 3) = 72 Reorder the terms: (3 + 4x)(3 + 4x) = 72 Multiply (3 + 4x) * (3 + 4x) (3(3 + 4x) + 4x * (3 + 4x)) = 72 ((3 * 3 + 4x * 3) + 4x * (3 + 4x)) = 72 ((9 + 12x) + 4x * (3 + 4x)) = 72 (9 + 12x + (3 * 4x + 4x * 4x)) = 72 (9 + 12x + (12x + 16x2)) = 72 Combine like terms: 12x + 12x = 24x (9 + 24x + 16x2) = 72 Solving 9 + 24x + 16x2 = 72 Solving for variable 'x'. Reorder the terms: 9 + -72 + 24x + 16x2 = 72 + -72 Combine like terms: 9 + -72 = -63 -63 + 24x + 16x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -63 + 24x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.9375 + 1.5x + x2 = 0 Move the constant term to the right: Add '3.9375' to each side of the equation. -3.9375 + 1.5x + 3.9375 + x2 = 0 + 3.9375 Reorder the terms: -3.9375 + 3.9375 + 1.5x + x2 = 0 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + 1.5x + x2 = 0 + 3.9375 1.5x + x2 = 0 + 3.9375 Combine like terms: 0 + 3.9375 = 3.9375 1.5x + x2 = 3.9375 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 3.9375 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 3.9375 + 0.5625 Combine like terms: 3.9375 + 0.5625 = 4.5 0.5625 + 1.5x + x2 = 4.5 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + 0.75) equal to 2.121320344 and -2.121320344.Subproblem 1
x + 0.75 = 2.121320344 Simplifying x + 0.75 = 2.121320344 Reorder the terms: 0.75 + x = 2.121320344 Solving 0.75 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.121320344 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.121320344 + -0.75 x = 2.121320344 + -0.75 Combine like terms: 2.121320344 + -0.75 = 1.371320344 x = 1.371320344 Simplifying x = 1.371320344Subproblem 2
x + 0.75 = -2.121320344 Simplifying x + 0.75 = -2.121320344 Reorder the terms: 0.75 + x = -2.121320344 Solving 0.75 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.121320344 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.121320344 + -0.75 x = -2.121320344 + -0.75 Combine like terms: -2.121320344 + -0.75 = -2.871320344 x = -2.871320344 Simplifying x = -2.871320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.371320344, -2.871320344}
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