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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 = 0 (-25 + 0 + 4x2) = 11x + 29 (-25 + 4x2) = 11x + 29 Reorder the terms: -25 + 4x2 = 29 + 11x Solving -25 + 4x2 = 29 + 11x Solving for variable 'x'. Reorder the terms: -25 + -29 + -11x + 4x2 = 29 + 11x + -29 + -11x Combine like terms: -25 + -29 = -54 -54 + -11x + 4x2 = 29 + 11x + -29 + -11x Reorder the terms: -54 + -11x + 4x2 = 29 + -29 + 11x + -11x Combine like terms: 29 + -29 = 0 -54 + -11x + 4x2 = 0 + 11x + -11x -54 + -11x + 4x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -54 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.5 + -2.75x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -2.75x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -2.75x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -2.75x + x2 = 0 + 13.5 -2.75x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -2.75x + x2 = 13.5 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 13.5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 13.5 + 1.890625 Combine like terms: 13.5 + 1.890625 = 15.390625 1.890625 + -2.75x + x2 = 15.390625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 15.390625 Calculate the square root of the right side: 3.923088707 Break this problem into two subproblems by setting (x + -1.375) equal to 3.923088707 and -3.923088707.Subproblem 1
x + -1.375 = 3.923088707 Simplifying x + -1.375 = 3.923088707 Reorder the terms: -1.375 + x = 3.923088707 Solving -1.375 + x = 3.923088707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 3.923088707 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 3.923088707 + 1.375 x = 3.923088707 + 1.375 Combine like terms: 3.923088707 + 1.375 = 5.298088707 x = 5.298088707 Simplifying x = 5.298088707Subproblem 2
x + -1.375 = -3.923088707 Simplifying x + -1.375 = -3.923088707 Reorder the terms: -1.375 + x = -3.923088707 Solving -1.375 + x = -3.923088707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -3.923088707 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -3.923088707 + 1.375 x = -3.923088707 + 1.375 Combine like terms: -3.923088707 + 1.375 = -2.548088707 x = -2.548088707 Simplifying x = -2.548088707Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.298088707, -2.548088707}
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