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Simplifying -1x2 + 14x + -44 = 0 Reorder the terms: -44 + 14x + -1x2 = 0 Solving -44 + 14x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 44 + -14x + x2 = 0 Move the constant term to the right: Add '-44' to each side of the equation. 44 + -14x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + -14x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -14x + x2 = 0 + -44 -14x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 -14x + x2 = -44 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -44 + 49 Reorder the terms: 49 + -14x + x2 = -44 + 49 Combine like terms: -44 + 49 = 5 49 + -14x + x2 = 5 Factor a perfect square on the left side: (x + -7)(x + -7) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -7) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -7 = 2.236067978 Simplifying x + -7 = 2.236067978 Reorder the terms: -7 + x = 2.236067978 Solving -7 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 2.236067978 + 7 Combine like terms: -7 + 7 = 0 0 + x = 2.236067978 + 7 x = 2.236067978 + 7 Combine like terms: 2.236067978 + 7 = 9.236067978 x = 9.236067978 Simplifying x = 9.236067978Subproblem 2
x + -7 = -2.236067978 Simplifying x + -7 = -2.236067978 Reorder the terms: -7 + x = -2.236067978 Solving -7 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -2.236067978 + 7 Combine like terms: -7 + 7 = 0 0 + x = -2.236067978 + 7 x = -2.236067978 + 7 Combine like terms: -2.236067978 + 7 = 4.763932022 x = 4.763932022 Simplifying x = 4.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.236067978, 4.763932022}
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