# ACT Math : How to find the solution to a quadratic equation

## Example Questions

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### Example Question #51 : Quadratic Equations

Solve for :

Possible Answers:

Correct answer:

Explanation:

With quadratic equations, you should always start by getting all of your terms to one side of the equation, setting this equal to :

Thus, simplify  into:

Now, the next question you need to ask yourself is, "Can this be factored?" In this case, it can, though we are sometimes a bit intimidated by  terms that have a coefficient like this. Factor the quadratic expression:

If you FOIL this out, you will see your original equation.

Now, remember that you merely need to set each group equal to . This gives you the two values for :

For the other group, you get .

### Example Question #41 : How To Find The Solution To A Quadratic Equation

Solve for :

Possible Answers:

Correct answer:

Explanation:

With quadratic equations, you should always start by getting all of your terms to one side of the equation, setting this equal to :

Thus, simplify  into:

Now, the next question you need to ask yourself is, "Can this be factored?" In this case, it cannot be easily factored. Therefore, you should use the quadratic formula. Recall that its general form is:

For our data, , and .

Thus, we have:

Simplifying, this is:

Now, simplify.

### Example Question #53 : Quadratic Equations

Solve for :

Possible Answers:

Correct answer:

Explanation:

With quadratic equations, you should always start by getting all of your terms to one side of the equation, setting this equal to :

Thus, simplify  into:

Now, the next question you need to ask yourself is, "Can this be factored?" In this case, it cannot be easily factored. Therefore, you should use the quadratic formula. Recall that its general form is:

For our data, , and .

Thus, we have:

Simplifying, this is:

Since  is negative, you know that there is no real solution (given the problems arising from the negative square root)!

### Example Question #581 : Algebra

Solve:

Possible Answers:

and

and

None of the other answers

and

and

Correct answer:

and

Explanation:

To solve, we must set it equal to zero. The above expression is of the form , so we can use the quadratic formula:

to solve for the roots which are  and

We can check by plugging the roots into the expression and making sure that it equals zero.

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