Question

How to solve the quadratic equation x^2 + 4x - 3 = 0?

Answer 1

To solve the quadratic equation \( x^2 + 4x - 3 = 0 \), we can use the quadratic formula:

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

In this case, the coefficients are:
- \( a = 1 \)
- \( b = 4 \)
- \( c = -3 \)

First, we need to calculate the discriminant (\( b^2 - 4ac \)):

\[
b^2 - 4ac = 4^2 - 4 \cdot 1 \cdot (-3) = 16 + 12 = 28
\]

Now, we can substitute the values into the quadratic formula:

\[
x = \frac{-4 \pm \sqrt{28}}{2 \cdot 1}
\]

Next, simplify \( \sqrt{28} \):

\[
\sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7}
\]

Now substitute \( \sqrt{28} \) back into the equation:

\[
x = \frac{-4 \pm 2\sqrt{7}}{2}
\]

This simplifies to:

\[
x = \frac{-4}{2} \pm \frac{2\sqrt{7}}{2}
\]
\[
x = -2 \pm \sqrt{7}
\]

Thus, the solutions are:

\[
x = -2 + \sqrt{7} \quad \text{and} \quad x = -2 - \sqrt{7}
\]

These are the two solutions to the quadratic equation \( x^2 + 4x - 3 = 0 \).