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Simplifying (2x + -1)(2x + 5) = 11 Reorder the terms: (-1 + 2x)(2x + 5) = 11 Reorder the terms: (-1 + 2x)(5 + 2x) = 11 Multiply (-1 + 2x) * (5 + 2x) (-1(5 + 2x) + 2x * (5 + 2x)) = 11 ((5 * -1 + 2x * -1) + 2x * (5 + 2x)) = 11 ((-5 + -2x) + 2x * (5 + 2x)) = 11 (-5 + -2x + (5 * 2x + 2x * 2x)) = 11 (-5 + -2x + (10x + 4x2)) = 11 Combine like terms: -2x + 10x = 8x (-5 + 8x + 4x2) = 11 Solving -5 + 8x + 4x2 = 11 Solving for variable 'x'. Reorder the terms: -5 + -11 + 8x + 4x2 = 11 + -11 Combine like terms: -5 + -11 = -16 -16 + 8x + 4x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -16 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 2x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 2x + x2)' equal to zero and attempt to solve: Simplifying -4 + 2x + x2 = 0 Solving -4 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2x + x2 = 0 + 4 2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2x + x2 = 4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 4 + 1 Reorder the terms: 1 + 2x + x2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2x + x2 = 5 Factor a perfect square on the left side: (x + 1)(x + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 1) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 1 = 2.236067978 Simplifying x + 1 = 2.236067978 Reorder the terms: 1 + x = 2.236067978 Solving 1 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.236067978 + -1 x = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 x = 1.236067978 Simplifying x = 1.236067978Subproblem 2
x + 1 = -2.236067978 Simplifying x + 1 = -2.236067978 Reorder the terms: 1 + x = -2.236067978 Solving 1 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.236067978 + -1 x = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 x = -3.236067978 Simplifying x = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.236067978, -3.236067978}Solution
x = {1.236067978, -3.236067978}
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