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Simplifying 242 = x2 + 14x Reorder the terms: 242 = 14x + x2 Solving 242 = 14x + x2 Solving for variable 'x'. Reorder the terms: 242 + -14x + -1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 242 + -14x + -1x2 = 0 + x2 + -1x2 242 + -14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 242 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -242 + 14x + x2 = 0 Move the constant term to the right: Add '242' to each side of the equation. -242 + 14x + 242 + x2 = 0 + 242 Reorder the terms: -242 + 242 + 14x + x2 = 0 + 242 Combine like terms: -242 + 242 = 0 0 + 14x + x2 = 0 + 242 14x + x2 = 0 + 242 Combine like terms: 0 + 242 = 242 14x + x2 = 242 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 = 242 + 49 Reorder the terms: 49 + 14x + x2 = 242 + 49 Combine like terms: 242 + 49 = 291 49 + 14x + x2 = 291 Factor a perfect square on the left side: (x + 7)(x + 7) = 291 Calculate the square root of the right side: 17.058722109 Break this problem into two subproblems by setting (x + 7) equal to 17.058722109 and -17.058722109.Subproblem 1
x + 7 = 17.058722109 Simplifying x + 7 = 17.058722109 Reorder the terms: 7 + x = 17.058722109 Solving 7 + x = 17.058722109 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 = 17.058722109 + -7 Combine like terms: 7 + -7 = 0 0 + x = 17.058722109 + -7 x = 17.058722109 + -7 Combine like terms: 17.058722109 + -7 = 10.058722109 x = 10.058722109 Simplifying x = 10.058722109Subproblem 2
x + 7 = -17.058722109 Simplifying x + 7 = -17.058722109 Reorder the terms: 7 + x = -17.058722109 Solving 7 + x = -17.058722109 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 = -17.058722109 + -7 Combine like terms: 7 + -7 = 0 0 + x = -17.058722109 + -7 x = -17.058722109 + -7 Combine like terms: -17.058722109 + -7 = -24.058722109 x = -24.058722109 Simplifying x = -24.058722109Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.058722109, -24.058722109}
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