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Simplifying 4x2 = 12x + 11 Reorder the terms: 4x2 = 11 + 12x Solving 4x2 = 11 + 12x Solving for variable 'x'. Reorder the terms: -11 + -12x + 4x2 = 11 + 12x + -11 + -12x Reorder the terms: -11 + -12x + 4x2 = 11 + -11 + 12x + -12x Combine like terms: 11 + -11 = 0 -11 + -12x + 4x2 = 0 + 12x + -12x -11 + -12x + 4x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -11 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -3x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -3x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -3x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -3x + x2 = 0 + 2.75 -3x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -3x + x2 = 2.75 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2.75 + 2.25 Combine like terms: 2.75 + 2.25 = 5 2.25 + -3x + x2 = 5 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -1.5) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -1.5 = 2.236067978 Simplifying x + -1.5 = 2.236067978 Reorder the terms: -1.5 + x = 2.236067978 Solving -1.5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.236067978 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.236067978 + 1.5 x = 2.236067978 + 1.5 Combine like terms: 2.236067978 + 1.5 = 3.736067978 x = 3.736067978 Simplifying x = 3.736067978Subproblem 2
x + -1.5 = -2.236067978 Simplifying x + -1.5 = -2.236067978 Reorder the terms: -1.5 + x = -2.236067978 Solving -1.5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.236067978 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.236067978 + 1.5 x = -2.236067978 + 1.5 Combine like terms: -2.236067978 + 1.5 = -0.736067978 x = -0.736067978 Simplifying x = -0.736067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.736067978, -0.736067978}
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