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Simplifying 3x(x + 5) + -11 = 9x + 12x + 1 Reorder the terms: 3x(5 + x) + -11 = 9x + 12x + 1 (5 * 3x + x * 3x) + -11 = 9x + 12x + 1 (15x + 3x2) + -11 = 9x + 12x + 1 Reorder the terms: -11 + 15x + 3x2 = 9x + 12x + 1 Reorder the terms: -11 + 15x + 3x2 = 1 + 9x + 12x Combine like terms: 9x + 12x = 21x -11 + 15x + 3x2 = 1 + 21x Solving -11 + 15x + 3x2 = 1 + 21x Solving for variable 'x'. Reorder the terms: -11 + -1 + 15x + -21x + 3x2 = 1 + 21x + -1 + -21x Combine like terms: -11 + -1 = -12 -12 + 15x + -21x + 3x2 = 1 + 21x + -1 + -21x Combine like terms: 15x + -21x = -6x -12 + -6x + 3x2 = 1 + 21x + -1 + -21x Reorder the terms: -12 + -6x + 3x2 = 1 + -1 + 21x + -21x Combine like terms: 1 + -1 = 0 -12 + -6x + 3x2 = 0 + 21x + -21x -12 + -6x + 3x2 = 21x + -21x Combine like terms: 21x + -21x = 0 -12 + -6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -2x + x2) = 0 Ignore the factor 3.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 = 3.236067978 x = 3.236067978 Simplifying x = 3.236067978Subproblem 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 = -1.236067978 x = -1.236067978 Simplifying x = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.236067978, -1.236067978}Solution
x = {3.236067978, -1.236067978}
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