Question

solve the quadratic equation
×2 + 3x - 5 = 0 basic form

Answer 1

To solve the quadratic equation \( x^2 + 3x - 5 = 0 \), we can use the quadratic formula:

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

In this equation, the coefficients are:

- \( a = 1 \) (the coefficient of \( x^2 \))
- \( b = 3 \) (the coefficient of \( x \))
- \( c = -5 \) (the constant term)

Now, we can substitute these values into the quadratic formula.

1. Compute the discriminant:

\[
b^2 - 4ac = 3^2 - 4(1)(-5) = 9 + 20 = 29
\]

2. Substitute into the quadratic formula:

\[
x = \frac{-3 \pm \sqrt{29}}{2 \times 1} = \frac{-3 \pm \sqrt{29}}{2}
\]

This gives us the two solutions:

\[
x_1 = \frac{-3 + \sqrt{29}}{2}
\]
\[
x_2 = \frac{-3 - \sqrt{29}}{2}
\]

So, the solutions to the equation \( x^2 + 3x - 5 = 0 \) are:

\[
x = \frac{-3 + \sqrt{29}}{2} \quad \text{and} \quad x = \frac{-3 - \sqrt{29}}{2}
\]