Question

Complete the square, solve the equation for x. x^2=24-4x. The answer is x= -2 ± 2√(7)

Answer 1

Step I: Rewrite your equation as x^2 + 4x + 24

Answer 2

Now take 1/2 of the b term (the 4) and square it. Add that number to both sides of the equation.

So 1/2 of 4 is 2; and 2 squared is 4.

We will add 4 to both sides of the equation, you get
x^2 + 4x + 4 = 24 + 4

Answer 3

The left side is a perfect square, so you have
(x + 2)^2 = 28

Answer 4

If (x + 2)^2 = 28, then x+2 = +/- sqrt (28)

Answer 5

so x = - 2 +/- sqrt (28)

Answer 6

Sqrt (28) = sqrt (4) times sqrt (7) = 2 sqrt (7)

Answer 7

So your final answer is - 2 +/- 2 sqrt (7)

Answer 8

Done.

Answer 9

Any questions?

Answer 10

thanks so much!

Answer 11

Welcome.

Answer 12

@Easyaspi314

Answer 13

Incorrect. Watch, I will show you.

Answer 14

2x^2 + 8x - 15 = 0

The very first step is to add 15 to both sides!

You have 2x^2 + 8x = 15

Answer 15

Now, you CANNOT take 1/2 of the b term and square it UNLESS you have the coefficient of x^2 being 1.
We have 2x^2. So FIRST, divide both sides by 2.

Answer 16

So we have x^2 + 4x = ,15/2

Answer 17

Now, that the coefficient of x^2 is 1, we NOW take 1/2 of the b term and square it. And we will add that number to both sides. So 1/2 of 4 is 2, and 2 squared is 4. We will add 4 to both sides.

Answer 18

So we have x^2 + 4x + 4 = 15/2 + 4
or x^2 + 4x + 4 = 11.5

Answer 19

wait where did 4x come from? it was 8x.

Answer 20

so x^2+8x+16=15/2+16 ?

Answer 21

We had 2x^2 + 8x on the left side, all what I did was divide both sides by 2, so you get x^2 + 4x.

Answer 22

OH i forgot about that step. okay that makes sense

Answer 23

So what I am saying is that if the left side was 3x^2 + 13x, we would have to first divide the left side by 3 and the right side by 3. What is critical is the coefficient of x^2 be 1. Thats a must.

Answer 24

So we have x^2 + 4x + 4 = 11.5

Answer 25

The left side is a perfect square, it is (x+2)^2

Answer 26

So, we have (x+2)^2 = 11.5, so x+ 2 = +/- sqrt (11.5)
so x = -2 +/- sqrt (11.5)

Answer 27

Done.

Answer 28

Make sure that each sense is crystal clear. Any questions, just write to me.

Answer 29

all of that makes sense to me. but the book has the answers in the back, thats why i have to show work, but it says the answer is x=-2±\[\left(\begin{matrix}\sqrt{46} \\ 2\end{matrix}\right)\]