Question

How do I solve this?

-6x-1+5x^2 = 8x^2

Thanks

Answer 1

Answer:

$\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}$

Or, by approximating:

$x\approx-0.1835\text{ or } x\approx -1.8165$

Step-by-step explanation:

Let’s convert this to standard form. We have:

$-6x-1+5x^2=8x^2$

Subtract 5x² from both sides:

$-6x-1=3x^2$

And add 6x and 1 to both sides:

$0=3x^2+6x+1$

This is not factorable. So, we will need to use the quadratic formula.

The quadratic formula for a quadratic in standard form is given by:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}$

In this case, a=3; b=6, and c=1.

Substitute appropriately:

$\displaystyle x=\frac{-6\pm\sqrt{6^2-4(3)(1)}}{2(3)}$

Simplify:

$\displaystyle x=\frac{-6\pm\sqrt{24}}{6}$

We can simplify the square root:

$\sqrt{24}=\sqrt{4}\cdot\sqrt{6}=2\sqrt{6}$

Hence:

$\displaystyle x=\frac{-6\pm2\sqrt{4}}{6}$

Simplify:

$\displaystyle x=\frac{-3\pm\sqrt{6}}{3}$

Hence, we will have two solutions:

$\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}$

Approximating them, we can see that our solutions are approximately:

$x\approx-0.1835\text{ or } x\approx -1.8165$