Question

Solve by using the Quadratic Formula3u^2 + 7u- 3= 0

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the quadratic equation

$3u^2+7u-3=0$

STEP 2: Write the needed terms

$\begin{gathered} By\text{ comparison with standard quadratic equation of the form:} \\ ax^2+bx+c=0 \\ a=3,b=7,c=-3 \end{gathered}$

STEP 3: Write the quadratic formula

$u_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

STEP 4: Substitute the values into the formula

$u_{1,2}=\frac{-7\pm\sqrt{7^2-4\cdot3\cdot(-3)}}{2\cdot3}$

STEP 5: Simplify:

$u_{1,2}=\frac{-7\pm\sqrt{49+36}}{6}=\frac{-7\pm\sqrt{85}}{6}$

STEP 6: Separate the solutions

$u_1=\frac{-7+\sqrt{85}}{6},u_2=\frac{-7-\sqrt{85}}{6}$

STEP 7: Simplify:

$\begin{gathered} u_1=0.369924076\approx0.37 \\ u_2=-2.70325741\approx-2.70 \end{gathered}$

Hence, the values of u are:

$\begin{gathered} 0.37 \\ -2.70 \end{gathered}$