# How do you solve 5x2-13x+6 Also how do you solve x2-36

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### 4 Answers

Solve `5x^2-13x+6`

First, set 2 sets of parentheses like so: ( )( )

In order to get `5x^2` we must break into factors. The only 2 factors that could work are `5x` and x.

Therefore we have: (5x - )(x - ). Both signs must be negative as middle term is negative and last is positive. Next we need 2 terms that multiply to equal 6. This can only be either 2 and 3 or 6 and 1.

Therefore we could have:

(5x-6)(x-1) or (5x-1)(x-6) or (5x-2)(x-3) or (5x-3)(x-2)

In order to determine the correct solution, you must find the sum the product of inner and outer terms.

Case 1 gives: -5x and -6x = -11x

Case 2 gives: -30x and -1x = -31x

Case 3 gives: -15x and -2x = -17x

Case 4 gives: -10x and -3x = -13x

The last instance is correct:

**The solution: `(5x-3)(x-2)` **

Solve `x^2-36` .

In this case you have no middle term, and the 2 given terms are perfect squares. This is a special case known as the difference of 2 squares.

( )( ) Same start, however keep in mind there is no middle term.

(x )(x ) to make the `x^2`

Next, since 36 is a perfect square identify the square root, which is 6.

(x 6)(x 6), since we want the middle term to "cancel out" each sign will be opposite.

`(x+6)(x-6)` Notice outer and inner terms are 6x and -6x which equal 0

**(x-6)(x+6) is your solution.**

How do you solve `5x^2-13x+6` ( `ax^2+bx+c` )

The first step of solving this is by multiplying a by c

`5 xx 6 = 30`

Then you find factors of 30 that add up to -13 (3 and 10) put those as b

`5x^2 - 10x - 3x + 6`

group

`(5x^2 - 10x) (- 3x + 6)`

Factor:

`5x (x - 2) -3 (x - 2 )`

`(5x - 3) (x - 2)`

the solutions are x = 3/5 and x = 2

Also how do you solve x2-36

For this one we use the difference of 2 squares (a - b)(a + b)

(x - 6) (x + 6)

5x²-13x+6

5x -3

1x -2

Therefore, 5x²-13x+6=(5x-3)(x-2)

When When

5x-3=0 x-2=0

5x=3 **x=2**

**x=3/5**

x²-36

1x +6

1x -6

Therefore, x²-36=(x+6)(x-6)

When When

x+6=0 x-6=0

**x=-6 x=6**

=5x2-13x+6

=5x2-10x-3x+6

=5x(x-2)-3(x-2)

=(x-2)(5x-3)

x2-36

=x^2 - 6^2

we know that a^2 - b^2 =(a+b)(a-b), so

=(x+6)(x-6)

Note ^ symbol used for power of the exponent .

I hope, it will really helpful to you.