To solve the quadratic equation 14x = 32 by completing the square, follow these steps:
1. Start with the equation in the form ax^2 + bx + c = 0. In this case, rewrite the given equation as 14x - 32 = 0.
2. Divide the entire equation by the coefficient of x^2 to have the coefficient of x^2 as 1. In this case, divide by 14 to get x - 32/14 = 0.
3. Move the constant term to the other side of the equation to isolate the x-term. The equation becomes x = 32/14.
4. Now, complete the square by adding and subtracting (b/2)^2 to the equation, where b is the coefficient of x. In this case, b = 1, so add and subtract (1/2)^2 = 1/4: x + 1/4 = 32/14.
5. Simplify the equation: x + 1/4 = 16/7.
6. Solve for x by taking the square root of both sides and simplify further if needed. The solution is x = ±√(16/7) - 1/4.
7. Finally, express the solution in simplified form.
After completing these steps, you will have solved the quadratic equation 14x = 32 by completing the square.
