To solve this equation, you must first eliminate the exponent from the by taking the square root of both sides: 

Since the square root of 36 could be either or , there must be 2 values of . So, solve for

and

to get solutions of .

When we factor, we are looking for two number that multiply to the constant, , and add to the middle term, . Looking through the factors of , we can find those factors to be  and .

Thus, we have the factors: 

.

To solve for the solutions, set each of these factors equal to zero.

Thus, we get , or .

Our second solution is, , or . 

From the zeroes we know

Use FOIL method to obtain:

FOIL the two factors to find the quadratic equation.

First terms:

Outer terms:

Inner terms:

Last terms:

Simplify:

Write the quadratic equation.

The equation  is in the form .

Substitute the proper coefficients into the quadratic equation.

The negative square root can be replaced by the imaginary term .  Simplify square root 60 by common factors of numbers with perfect squares.

Simplify the fraction.

A possible root is:   

Pull out a common factor of negative four.

The term inside the parentheses can be factored.

Set the binomials equal to zero and solve for the roots.  We can ignore the negative four coefficient.

The answers are:  

Factoring a quadratic equation means doing FOIL backwards. Recall that when you use FOIL, you start with two binomials and end with a trinomial:

Now, we're trying to go the other direction -- starting with a trinomial, and going back to two factors.

Here, -3 is equal to , and -2 is equal to . We can use this information to find out what and  are, separately. In other words, we have to find two factors of -3 that add up to -2.

Factors of -3:

• 3*-1 (sum = 2)
• -3*1 (sum = -2)

Thus our factored equation should look like this:

The roots of the quadratic equation are the values of x for which y is 0.

We know that anything times zero is zero. So the entire expression equals zero when at least one of the factors equals zero.

Factor:

Double check by factoring:

Add together:

Therefore:

1) Split up the middle term so that factoring by grouping is possible.

Factors of 10 include:

1 * 10= 10    1 + 10 = 11

2 * 5 =10      2 + 5 = 7

–2 * –5 = 10    –2 + –5 = –7 Good!

2) Now factor by grouping, pulling "x" out of the first pair and "-5" out of the second.

3) Now pull out the common factor, the "(x-2)," from both terms.

4) Set both terms equal to zero to find the possible roots and solve using inverse operations.

x – 5 = 0,  x = 5

x – 2 = 0, x = 2

1) First step of solving any equation: combine like terms. With quadratics, the easiest step to take is to set the expression equal to zero.

2) There are two ways to do this problem. The first and most intuitive method is standard factoring.

16 + 1 = 17

8 + 2 = 10

4 + 4 = 8

3) Then follow the usual steps, pulling out the common factor from both pairs, "x" from the first and "4" from the second.

4) Pull out the "(x+4)" to wind up with:

5) Set each term equal to zero.

x + 4 = 0, x = –4

But there's a shortcut! Assuming the terms are arranged by descending degree (i.e., ), and the third term is both a perfect square whose square root is equal to half of the middle term, mathematicians use a little trick. In this case, the square root of 16 is 4. 4 * 2=8, so the trick will work. Take the square root of the first and last term, then stick a plus sign in between them and square the parentheses. 

And x, once again, is equal to –4.