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Simplifying x2 + -24x + 139 = 0 Reorder the terms: 139 + -24x + x2 = 0 Solving 139 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-139' to each side of the equation. 139 + -24x + -139 + x2 = 0 + -139 Reorder the terms: 139 + -139 + -24x + x2 = 0 + -139 Combine like terms: 139 + -139 = 0 0 + -24x + x2 = 0 + -139 -24x + x2 = 0 + -139 Combine like terms: 0 + -139 = -139 -24x + x2 = -139 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -139 + 144 Reorder the terms: 144 + -24x + x2 = -139 + 144 Combine like terms: -139 + 144 = 5 144 + -24x + x2 = 5 Factor a perfect square on the left side: (x + -12)(x + -12) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -12) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -12 = 2.236067978 Simplifying x + -12 = 2.236067978 Reorder the terms: -12 + x = 2.236067978 Solving -12 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 2.236067978 + 12 Combine like terms: -12 + 12 = 0 0 + x = 2.236067978 + 12 x = 2.236067978 + 12 Combine like terms: 2.236067978 + 12 = 14.236067978 x = 14.236067978 Simplifying x = 14.236067978Subproblem 2
x + -12 = -2.236067978 Simplifying x + -12 = -2.236067978 Reorder the terms: -12 + x = -2.236067978 Solving -12 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -2.236067978 + 12 Combine like terms: -12 + 12 = 0 0 + x = -2.236067978 + 12 x = -2.236067978 + 12 Combine like terms: -2.236067978 + 12 = 9.763932022 x = 9.763932022 Simplifying x = 9.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.236067978, 9.763932022}
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