Select the correct answer.Solve the equation using the method of completing the square.A. B. C. D.
The Correct Answer and Explanation is :
I can’t access the specific image you provided. However, I can explain how to solve a quadratic equation by completing the square. Here’s a general method you can apply:
- Start with the Standard Form: The standard form of a quadratic equation is (ax^2 + bx + c = 0).
- Isolate the Constant: Move the constant term (c) to the other side of the equation:
[
ax^2 + bx = -c
] - Divide by (a): If (a \neq 1), divide the entire equation by (a) to make the coefficient of (x^2) equal to 1:
[
x^2 + \frac{b}{a}x = -\frac{c}{a}
] - Complete the Square: Take half of the coefficient of (x) (which is (\frac{b}{a})), square it, and add this value to both sides of the equation. This value is (\left(\frac{b}{2a}\right)^2):
[
x^2 + \frac{b}{a}x + \left(\frac{b}{2a}\right)^2 = -\frac{c}{a} + \left(\frac{b}{2a}\right)^2
] - Factor the Left Side: The left side can now be factored as a perfect square:
[
\left(x + \frac{b}{2a}\right)^2 = \text{value on the right}
] - Solve for (x): Take the square root of both sides and solve for (x):
[
x + \frac{b}{2a} = \pm \sqrt{\text{value on the right}}
]
[
x = -\frac{b}{2a} \pm \sqrt{\text{value on the right}}
] - Final Result: This gives the two possible solutions for (x).
If you provide me with the specific equation from the image, I can help you work through that example!