How do you solve 2x^2+11x-6=0 using the quadratic formula?

1 Answer
Dec 26, 2016

The two solutions are x = 0.50 and x = -6

Explanation:

Since this question is given in standard form, meaning that it follows the form: ax^(2) + bx + c = 0, we can use the quadratic formula to solve for x:
https://mathbitsnotebook.com/Algebra1/Quadratics/QDquadform.htmlhttps://mathbitsnotebook.com/Algebra1/Quadratics/QDquadform.html

I think it's worthwhile to mention that a is the number that has the x^2 term associated with it. Thus, it would be 2x^(2) for this question.b is the number that has the x variable associated with it and it would be 11x, and c is a number by itself and in this case it is -6.

Now, we just plug our values into the equation like this:

x = (- (11) +- sqrt((11)^(2) - 4(2)(-6)))/(2(2))

x = (-11 +-sqrt(121+48))/4

x = (-11 +- sqrt(169))/4

For these type of problems, you will obtain two solutions because of the +- part. So what you want to do is add -11 to sqrt(169) together and divide that by 4:

x = (-11+sqrt(169))/4
x = 2/4= 0.50

Now, we subtract sqrt(169) from -11 and divide by 4:

x = (-11-sqrt(169))/4
x = -24/4 = -6

Therefore, the two possible solutions are:
x = 0.5 and x = -6