Please show the procedure for answering this quadratic equation using the completing the square method:
x^2+14x+98
I think i understand the basics of the method, but in this particular question I'm finding it hard to use the appropriate factors of 98 - 7 and 14 - to factorize 14x.
x^2 + 14 x + 98 = 0 I assume
x^2 + 14 x = -98
14/2 = 7
7^2 = 49
x^2 + 14 x + 49 = -98 + 49
(x+7)^2 = -49
square root of a negative number is imaginary
x+7 = -7i or + 7i
x = -7 -7i = -7 (1+i)
or
x = -7 + 7i = -7 (1-i)
To solve the quadratic equation using the completing the square method, follow these steps:
1. Write the equation in the form ax^2 + bx + c = 0. In this case, we have x^2 + 14x + 98 = 0.
2. Divide the equation by the coefficient of x^2 so that the coefficient becomes 1. Since the coefficient of x^2 is already 1 in this case, we don't need to perform this step.
3. Move the constant term to the other side of the equation. Subtract 98 from both sides: x^2 + 14x = -98.
4. To complete the square, add the square of half the coefficient of x to both sides of the equation. The coefficient of x is 14, so half of it is 7. Add (7^2) = 49 to both sides: x^2 + 14x + 49 = -98 + 49.
5. Simplify the equation: x^2 + 14x + 49 = -49.
6. Factorize the left side of the equation. Since the left side is a perfect square trinomial, it can be factored as (x + 7)^2.
7. Simplify the right side of the equation: -98 + 49 = -49.
8. The equation becomes (x + 7)^2 = -49.
9. Take the square root of both sides to eliminate the square: x + 7 = sqrt(-49).
10. Since the square root of a negative number is not a real number, there are no real solutions to this equation.
In summary, the equation x^2 + 14x + 98 = 0 cannot be solved using the completing the square method because it does not have any real solutions.