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Simplifying 0 = x2 + -14x + 41 Reorder the terms: 0 = 41 + -14x + x2 Solving 0 = 41 + -14x + x2 Solving for variable 'x'. Combine like terms: 0 + -41 = -41 -41 + 14x + -1x2 = 41 + -14x + x2 + -41 + 14x + -1x2 Reorder the terms: -41 + 14x + -1x2 = 41 + -41 + -14x + 14x + x2 + -1x2 Combine like terms: 41 + -41 = 0 -41 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -41 + 14x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -41 + 14x + -1x2 = 0 + x2 + -1x2 -41 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -41 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 41 + -14x + x2 = 0 Move the constant term to the right: Add '-41' to each side of the equation. 41 + -14x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -14x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -14x + x2 = 0 + -41 -14x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -14x + x2 = -41 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 = -41 + 49 Reorder the terms: 49 + -14x + x2 = -41 + 49 Combine like terms: -41 + 49 = 8 49 + -14x + x2 = 8 Factor a perfect square on the left side: (x + -7)(x + -7) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -7) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -7 = 2.828427125 Simplifying x + -7 = 2.828427125 Reorder the terms: -7 + x = 2.828427125 Solving -7 + x = 2.828427125 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 = 2.828427125 + 7 Combine like terms: -7 + 7 = 0 0 + x = 2.828427125 + 7 x = 2.828427125 + 7 Combine like terms: 2.828427125 + 7 = 9.828427125 x = 9.828427125 Simplifying x = 9.828427125Subproblem 2
x + -7 = -2.828427125 Simplifying x + -7 = -2.828427125 Reorder the terms: -7 + x = -2.828427125 Solving -7 + x = -2.828427125 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 = -2.828427125 + 7 Combine like terms: -7 + 7 = 0 0 + x = -2.828427125 + 7 x = -2.828427125 + 7 Combine like terms: -2.828427125 + 7 = 4.171572875 x = 4.171572875 Simplifying x = 4.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.828427125, 4.171572875}
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