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Simplifying x2 + 14x + 49 = 5 Reorder the terms: 49 + 14x + x2 = 5 Solving 49 + 14x + x2 = 5 Solving for variable 'x'. Reorder the terms: 49 + -5 + 14x + x2 = 5 + -5 Combine like terms: 49 + -5 = 44 44 + 14x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 44 + 14x + x2 = 0 Begin completing the square. 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 = -4.763932022 x = -4.763932022 Simplifying x = -4.763932022Subproblem 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 = -9.236067978 x = -9.236067978 Simplifying x = -9.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.763932022, -9.236067978}
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