Question

Solve equation by the quadratic formula. List the solutions, separated by commas. 4r^2 +3r+10=8

Answer 1

Answer:

$-\frac{3}{8} +\frac{\sqrt[]{23}i }{8},-\frac{3}{8} -\frac{\sqrt[]{23}i }{8}$

or

$-0.375+0.599479i,-0.375-0.599479i$

Step-by-step 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,

$r=-\frac{3}{8} \frac{+}{}\frac{\sqrt[]{23}*\sqrt[]{-1} }{8}$

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

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