The equation in the image is:

$x^2 = 4x + 12$

Solution:

We can solve this quadratic equation by rearranging it into standard form:

$x^2 - 4x - 12 = 0$

Now, use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Here:

• $a = 1$
• $b = -4$
• $c = -12$

Substitute these values into the quadratic formula:

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-12)}}{2(1)}$

$x = \frac{4 \pm \sqrt{16 + 48}}{2}$

$x = \frac{4 \pm \sqrt{64}}{2}$

$x = \frac{4 \pm 8}{2}$

Solve for the two possible values of $x$:

1. $x = \frac{4 + 8}{2} = \frac{12}{2} = 6$
2. $x = \frac{4 - 8}{2} = \frac{-4}{2} = -2$

Final Answer:

The solutions are: $x = 6 \quad \text{and} \quad x = -2$

Would you like further details or a graphical representation of the solution?

Related Questions:

1. How do you graph quadratic equations like this one?
2. What is the significance of the discriminant in solving quadratic equations?
3. How do you factorize quadratic equations, and is it possible for this one?
4. Can we solve this equation using completing the square?
5. How do we interpret the solutions of this equation in a real-world context?

Tip:

When solving quadratic equations, always check if factoring is quicker before using the quadratic formula!