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Simplifying (2x + 5)(2x + 5) = 11x + 29 Reorder the terms: (5 + 2x)(2x + 5) = 11x + 29 Reorder the terms: (5 + 2x)(5 + 2x) = 11x + 29 Multiply (5 + 2x) * (5 + 2x) (5(5 + 2x) + 2x * (5 + 2x)) = 11x + 29 ((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = 11x + 29 ((25 + 10x) + 2x * (5 + 2x)) = 11x + 29 (25 + 10x + (5 * 2x + 2x * 2x)) = 11x + 29 (25 + 10x + (10x + 4x2)) = 11x + 29 Combine like terms: 10x + 10x = 20x (25 + 20x + 4x2) = 11x + 29 Reorder the terms: 25 + 20x + 4x2 = 29 + 11x Solving 25 + 20x + 4x2 = 29 + 11x Solving for variable 'x'. Reorder the terms: 25 + -29 + 20x + -11x + 4x2 = 29 + 11x + -29 + -11x Combine like terms: 25 + -29 = -4 -4 + 20x + -11x + 4x2 = 29 + 11x + -29 + -11x Combine like terms: 20x + -11x = 9x -4 + 9x + 4x2 = 29 + 11x + -29 + -11x Reorder the terms: -4 + 9x + 4x2 = 29 + -29 + 11x + -11x Combine like terms: 29 + -29 = 0 -4 + 9x + 4x2 = 0 + 11x + -11x -4 + 9x + 4x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -4 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 2.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 2.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2.25x + x2 = 0 + 1 2.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2.25x + x2 = 1 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 1 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 1 + 1.265625 Combine like terms: 1 + 1.265625 = 2.265625 1.265625 + 2.25x + x2 = 2.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + 1.125) equal to 1.505199322 and -1.505199322.Subproblem 1
x + 1.125 = 1.505199322 Simplifying x + 1.125 = 1.505199322 Reorder the terms: 1.125 + x = 1.505199322 Solving 1.125 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.505199322 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.505199322 + -1.125 x = 1.505199322 + -1.125 Combine like terms: 1.505199322 + -1.125 = 0.380199322 x = 0.380199322 Simplifying x = 0.380199322Subproblem 2
x + 1.125 = -1.505199322 Simplifying x + 1.125 = -1.505199322 Reorder the terms: 1.125 + x = -1.505199322 Solving 1.125 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.505199322 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.505199322 + -1.125 x = -1.505199322 + -1.125 Combine like terms: -1.505199322 + -1.125 = -2.630199322 x = -2.630199322 Simplifying x = -2.630199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.380199322, -2.630199322}
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