Question

x2 + 7x - 6 = 2

Answer 1

\[x^2 +7x - 6 = 2\]
is this what you meant?

Answer 2

Transposing 2 to the left side you'll have
\[x^2 + 7x - 6 - 2 =0\]
Combine like terms
\[x^2 + 7x - 8 = 0\]
Now try to think of factors of -8 which when added is equal to 7
What could be the factors?

Answer 3

@BethFraser2000

Answer 4

\[ x^2 +7x -6-2=0\]\[x^2 +7x -8=0\]\[(x^2 +7x) -8 =0\]\[\left(x^2 +7x +\frac{49}{4}\right)-8-\frac{49}{4}=0\]\[\left(x+\frac{7}{2}\right)^2 = \frac{81}{4}\]\[\sqrt{\left(x+\frac{7}{2}\right)^2} = \pm \sqrt{\frac{81}{4}}\]\[x+\frac{7}{2} = \pm \frac{9}{2}\]

Answer 5

For complex numbers such as these, it's easier to use methods such as completing the square , or even the quadratic formula in solving for values of x.

Answer 6

Now you see you'll end up getting two values for x:\[x=\frac{9}{2} -\frac{7}{2}\]\[x= -\frac{9}{2} -\frac{7}{2}\]

Answer 7

In simple manner, you just have to think of the factors of -8 such that when added will have a sum of 7.
Factors of -8
1 and -8
-1 and 8
2 and -4
-2 and 4
Checking for the sum:
1 + -8 = -7
-1 + 8 = 7
2 + -4 = -2
-2 + 4 = 2
So you will have the factors as -1 and 8
(x-1)(x+8)=0
x-1=0
x = 1
x+8=0
x=-8

Answer 8

The other method is the quadratic formula method: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] Our formula follows the format \(\color{red}ax^2+\color{blue}by+c=0\), therefore our a= 1, b= 7, c = -8\[x = \frac{-(7) \pm \sqrt{(7)^2 - 4(1)(-8)}}{2(1)}\]\[x= \frac{-7 \pm \sqrt{49 -32}}{2}\]\[x = \frac{-7 \pm \sqrt{17}}{2}\]\[x= \frac{-7 +\sqrt{17}}{2} \ ,\ \ x= \frac{-7 - \sqrt{17}}{2}\]

Answer 9

Might have made some kind of error there, so feel free to correct me there :)

Answer 10

Awesome, we have like 3 separate methods of solving the same problem!

Answer 11

x^2 +7x−8=0

(x+8)(x-1)=0

x has 2 integer solutions - I think there must be mistakes in your solutions above....

Answer 12

Well, just the quadratic perhaps. One thing you will notice is i did not completely solve it out for her, therefore my first method has answers that need to be reduced.

Answer 13

You have made a mistake in the quadratic formula : you missed a - in the discriminant

Answer 14

@MrNood @Jhannybean 's use of completing the square to solve this quadratic yields the same result you got by factoring. There is not an error. The Quadratic Formula has its origin in completing the square. Just saying.

Answer 15

@Directrix
Since his formula results in incorrect results (i.e no integer results) there IS an error.

he has miscalculated the discriminant - by missing a "-" sign.

There is an error - just saying

Answer 16

@MrNood I got integer results. (See attachment.) Not that @Jhannybean did not employ the Quadratic Formula but used the technique of completing the square.

Answer 17

Looking back I can see where I went wrong. \[x = \frac{-(7) \pm \sqrt{(7)^2 - 4(1)(-8)}}{2(1)}\]\[x= \frac{-7 \pm \sqrt{49 +32}}{2}\]\[x = \frac{-7 \pm \sqrt{81}}{2}\]\[x= \frac{-7\pm 9}{2}\]

Answer 18

This thread illustrates what I think OpenStudy is meant to be - a civil discussion about a particular mathematics problem showing multiple solutions, and error diagnosis.
@Jhannybean @MrNood Let's do it again soon.