Question

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

Answer 1

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)=(-b\pm√(b^2-4ac))/(2a)`

STEP 4: Substitute the values into the formula

`u_(1,2)=(-7\pm√(7^2-4\cdot3\cdot(-3)))/(2\cdot3)`

STEP 5: Simplify:

`u_(1,2)=(-7\pm√(49+36))/(6)=(-7\pm√(85))/(6)`

STEP 6: Separate the solutions

`u_1=(-7+√(85))/(6),u_2=(-7-√(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}`