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Simplifying (2x + 5)(2x + 5) = 18 Reorder the terms: (5 + 2x)(2x + 5) = 18 Reorder the terms: (5 + 2x)(5 + 2x) = 18 Multiply (5 + 2x) * (5 + 2x) (5(5 + 2x) + 2x * (5 + 2x)) = 18 ((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = 18 ((25 + 10x) + 2x * (5 + 2x)) = 18 (25 + 10x + (5 * 2x + 2x * 2x)) = 18 (25 + 10x + (10x + 4x2)) = 18 Combine like terms: 10x + 10x = 20x (25 + 20x + 4x2) = 18 Solving 25 + 20x + 4x2 = 18 Solving for variable 'x'. Reorder the terms: 25 + -18 + 20x + 4x2 = 18 + -18 Combine like terms: 25 + -18 = 7 7 + 20x + 4x2 = 18 + -18 Combine like terms: 18 + -18 = 0 7 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 5x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 5x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 5x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 5x + x2 = 0 + -1.75 5x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 5x + x2 = -1.75 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -1.75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -1.75 + 6.25 Combine like terms: -1.75 + 6.25 = 4.5 6.25 + 5x + x2 = 4.5 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + 2.5) equal to 2.121320344 and -2.121320344.Subproblem 1
x + 2.5 = 2.121320344 Simplifying x + 2.5 = 2.121320344 Reorder the terms: 2.5 + x = 2.121320344 Solving 2.5 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.121320344 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.121320344 + -2.5 x = 2.121320344 + -2.5 Combine like terms: 2.121320344 + -2.5 = -0.378679656 x = -0.378679656 Simplifying x = -0.378679656Subproblem 2
x + 2.5 = -2.121320344 Simplifying x + 2.5 = -2.121320344 Reorder the terms: 2.5 + x = -2.121320344 Solving 2.5 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.121320344 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.121320344 + -2.5 x = -2.121320344 + -2.5 Combine like terms: -2.121320344 + -2.5 = -4.621320344 x = -4.621320344 Simplifying x = -4.621320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.378679656, -4.621320344}
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