Question

Solve x^2 + 5x – 3 = 0 using the quadratic formula.

Answer 1

The quadratic formula is:

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

For a quadratic equation in standard form:

`ax^2+bx+c=0`

In this case, we have:

`\begin{gathered} a=1 \\ b=5 \\ c=-3 \end{gathered}`
`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-5\pm\sqrt[]{(5)^2-4(1)(-3)}}{2(1)} \\ x=\frac{-5\pm\sqrt[]{25+12}}{2} \\ x=\frac{-5\pm\sqrt[]{37}}{2} \end{gathered}`

The given quadratic equation has two solutions:

• First one

`\begin{gathered} x_1=\frac{-5+\sqrt[]{37}}{2} \\ x_1=-(5)/(2)+\frac{\sqrt[]{37}}{2} \end{gathered}`

• Second one

`\begin{gathered} x_2=\frac{-5-\sqrt[]{37}}{2} \\ x_2=-(5)/(2)-\frac{\sqrt[]{37}}{2} \end{gathered}`

Therefore, the solutions of the given quadratic equation are:

`$$\boldsymbol{x=-(5)/(2)+\frac{\sqrt[]{37}}{2}}$$,$$\boldsymbol{x=-(5)/(2)-\frac{\sqrt[]{37}}{2}}$$`