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Simplifying 108 = 14x + x2 Solving 108 = 14x + x2 Solving for variable 'x'. Reorder the terms: 108 + -14x + -1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 108 + -14x + -1x2 = 0 + x2 + -1x2 108 + -14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 108 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -108 + 14x + x2 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + 14x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 14x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 14x + x2 = 0 + 108 14x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 14x + x2 = 108 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 = 108 + 49 Reorder the terms: 49 + 14x + x2 = 108 + 49 Combine like terms: 108 + 49 = 157 49 + 14x + x2 = 157 Factor a perfect square on the left side: (x + 7)(x + 7) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (x + 7) equal to 12.529964086 and -12.529964086.Subproblem 1
x + 7 = 12.529964086 Simplifying x + 7 = 12.529964086 Reorder the terms: 7 + x = 12.529964086 Solving 7 + x = 12.529964086 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 = 12.529964086 + -7 Combine like terms: 7 + -7 = 0 0 + x = 12.529964086 + -7 x = 12.529964086 + -7 Combine like terms: 12.529964086 + -7 = 5.529964086 x = 5.529964086 Simplifying x = 5.529964086Subproblem 2
x + 7 = -12.529964086 Simplifying x + 7 = -12.529964086 Reorder the terms: 7 + x = -12.529964086 Solving 7 + x = -12.529964086 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 = -12.529964086 + -7 Combine like terms: 7 + -7 = 0 0 + x = -12.529964086 + -7 x = -12.529964086 + -7 Combine like terms: -12.529964086 + -7 = -19.529964086 x = -19.529964086 Simplifying x = -19.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.529964086, -19.529964086}
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