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

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baxthum8 eNotes educator| Certified Educator

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.

atyourservice | Student

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`


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


`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)

imyounger2 | Student


5x         -3

1x         -2

Therefore, 5x²-13x+6=(5x-3)(x-2)

When                    When

5x-3=0                x-2=0

5x=3                    x=2



1x  +6

1x  -6

Therefore, x²-36=(x+6)(x-6)

When                    When

x+6=0                  x-6=0

x=-6                    x=6

yousafbhutta86 | Student






=x^2 - 6^2

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


Note ^ symbol used for power of the exponent .

I hope, it will really helpful to you.

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