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Simplifying 0 = x2 + -8x + 11 Reorder the terms: 0 = 11 + -8x + x2 Solving 0 = 11 + -8x + x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + 8x + -1x2 = 11 + -8x + x2 + -11 + 8x + -1x2 Reorder the terms: -11 + 8x + -1x2 = 11 + -11 + -8x + 8x + x2 + -1x2 Combine like terms: 11 + -11 = 0 -11 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2 -11 + 8x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 -11 + 8x + -1x2 = 0 + x2 + -1x2 -11 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -11 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -8x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -8x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -8x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8x + x2 = 0 + -11 -8x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -8x + x2 = -11 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -11 + 16 Reorder the terms: 16 + -8x + x2 = -11 + 16 Combine like terms: -11 + 16 = 5 16 + -8x + x2 = 5 Factor a perfect square on the left side: (x + -4)(x + -4) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -4) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -4 = 2.236067978 Simplifying x + -4 = 2.236067978 Reorder the terms: -4 + x = 2.236067978 Solving -4 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.236067978 + 4 x = 2.236067978 + 4 Combine like terms: 2.236067978 + 4 = 6.236067978 x = 6.236067978 Simplifying x = 6.236067978Subproblem 2
x + -4 = -2.236067978 Simplifying x + -4 = -2.236067978 Reorder the terms: -4 + x = -2.236067978 Solving -4 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.236067978 + 4 x = -2.236067978 + 4 Combine like terms: -2.236067978 + 4 = 1.763932022 x = 1.763932022 Simplifying x = 1.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.236067978, 1.763932022}
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