18.0k views
0 votes
How do I solve this?

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

Thanks

1 Answer

6 votes

Answer:


\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

User EComEvo
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories