Question

How do I solve this?

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

Thanks

Answer 1

`\displaystyle x=(-3+√(6))/(3)\text{ and } x=(-3-√(6))/(3)`

Or, by approximating:

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

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=(-b\pm√(b^2-4ac))/(2a)}`

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

Substitute appropriately:

`\displaystyle x=(-6\pm√(6^2-4(3)(1)))/(2(3))`

Simplify:

`\displaystyle x=(-6\pm√(24))/(6)`

We can simplify the square root:

`√(24)=√(4)\cdot√(6)=2√(6)`

Hence:

`\displaystyle x=(-6\pm2√(4))/(6)`

Simplify:

`\displaystyle x=(-3\pm√(6))/(3)`

Hence, we will have two solutions:

`\displaystyle x=(-3+√(6))/(3)\text{ and } x=(-3-√(6))/(3)`

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

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