Question

Hello, I need some serious help with these questions by completing the square (Please do step by step instructions):
1. X^2 + 6x + 34 = 0
2. 2X^2 + 16X + 42 = 0
3. 4X^2 - 7X - 2 = 0
4. 2X^2 + 9X + 4 = 0
5. A rectangular pool has an area of 880 ft^2. The length is 10 feet longer than the width. Find the dimensions of the pool. Solve by completing the square. Round answers to the nearest tenth of a foot.
6. A small painting has an area of 400cm^2. The length is 4 more than 2 times the width. Find the dimensions of the painting. Solve by completing the square. Round answers to the nearest

Answer 1

what do you need to do with the first 4?

Answer 2

You need to find solve for X by completing the square.

Answer 3

1) x^2 +6x +34=0
x^2 + 6x +__= -34
x^2 +6x+ 9= -34+9
X^2 +6x +9+ -25
(x+3)^2 = -25
No solution^

Answer 4

yes, you have done correctly

Answer 5

Can anyone help me with the rest tho? I'm not sure how they will work out....I've done a lot of problems similar to this idea, but my teacher never taught us how to solve equations like the ones above. Please Help

Answer 6

2,3,4..similar problems, complete the squares

Answer 7

for the last 2 questions, you have to form equations to solve.
5. say, the width of the pool is x feet, then length=x+10
so, area= x(x+10)=x^2+10x=800 (given)
solve
6.say the width is x cm, then length=2x+4 cm
so, area= x(2x+4)= 2x^2+4x=400 (given)
solve

Answer 8

2.) 2X^2 + 16X + 42 = 0; subtract the C term (48) from both sides
2X^2 + 16X = -42; b/2^2; getting 64- add 64 to both sides
2X^2 +16X + 64 = 22
22 = (x + 64)^2; take the square root
√22= (x+64)
Problem unsolvable?

Answer 9

Second problem:
2X^2 + 16X + 42 = 0
I'd start by factoring out the common factor, 2:

2(x^2 + 8x + 21)=0

Focus on the x^2 + 8x + 21 part.
This is important: Take half of the coefficient (8) of the x term; square it: (8/x)^2 = 4^2 = 16

Add, then subtract this result (4) as follows:

x^2 + 8x + 16 - 16 +21 = 0

Now the first 3 terms constitute a perfect square, and should be re-written as the square of a binomial; the last 2 terms, -16 and +21, combine to 5:
(x + 4)^2 + 5 = 0

We need to solve for x+4, so subtract 5 from both sides to obtain

(x+4)^2 = -5

Taking the square root of both sides, x+4 = (plus or minus) Sqrt(-5).

Subtract 4 from both sides:

x = -4 (plus or minus) i*Sqrt(5)

This yields the two (complex) roots of this equation.

A reminder: Sqrt (-1) = i, so
Sqrt(-5) = i*Sqrt(5)

You can solve Equations 3 and 4 in the same general manner. If this process is not clear to you, please ask appropriate questions.

Answer 10

I see you've tried to solve this problem on your own and commend you for having done so. My strong suggestion is that you factor out that common factor of 2 BEFORE attempting to "complete the square."

Answer 11

Okay, thank you so much....I'm still trying to get used to all this :)

Answer 12

"You can solve Equations 3 and 4 in the same general manner." I've thought all along that your instructions were to solve all four equations using completing the square. You could, of course, try solving them using other methods, to check the outcomes of your "completing the square" approach.

Answer 13

Ok, thanks for the clarification