Question

Solve equation by the quadratic formula. List the solutions, separated by commas.

4r^2 +3r+10=8

Answer 1

`-(3)/(8) +\frac{\sqrt[]{23}i }{8},-(3)/(8) -\frac{\sqrt[]{23}i }{8}`

or

`-0.375+0.599479i,-0.375-0.599479i`

Explanation:

`4r^2+3r+10=8`

Bring the 8 to the left side so that we equal the equation to 0. To do this, simply substract 8 on both sides.

`4r^2+3r+10-8=8-8\\4r^2+3r+2=0`

Where;

`a=4\\b=3\\c=2`

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

Replace. Let x be r

`r=\frac{-3\frac{+}{}\sqrt[]{(3)^2-4(4)(2)} }{2(4)}`

`r=\frac{-3\frac{+}{}\sqrt[]{9-32} }{8}`

`r=\frac{-3\frac{+}{}\sqrt[]{-23} }{8}`

It has no real solution because the square root is negative.

We can say that,

`r=-(3)/(8) \frac{+}{}\frac{\sqrt[]{23}*\sqrt[]{-1} }{8}`

`r=-(3)/(8) \frac{+}{}\frac{\sqrt[]{23}i }{8}`

`r_1=-0.375+0.599479i\\r_2=-0.375-0.599479i`