Find the solutions to the equation by completing the square x^2-6x=7
1 answer:
The answers are x=7 and x=-1
Look at my photo for the work. I’m not sure if that’s exactly “completing the square”, (sorry I did my best) but the method I did in this works better for me.
What I find helps is when you multiply the coefficient of the first term (in this case 1 in the 1x^2) by the last term (-7). Then, find factors of -7 that add to the middle term (-6). The factors I found were 1 and -7. Then substitute them into the equation so it’s x^2 + 1x-7x -7=0. The value of the equation stays the same, except now you are able to group.
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Answer: A. x= 5"
Step-by-step explanation:
ORIGINAL/NEW = 11"/7" = 8.5"/x
x = 7" x 8.5"/11" = 59.5"/11 = 5.409 ≅ 5.41"
If we wanted to keep most of the engraving, we would adjust the larger dimension, but we have been asked to adjust one dimension to 5", since it is said that C. x = 5.41 is incorrect
Then we will adjust the minor dimension to 5"
ORIGINAL/NEW = 11"/y = 8.5"/5"
y= 11" x 5"/8.5" = 6.47"
Then new dimensions of the paper are 6.47" x 5" to fit an 7" x 5" frame
Answer: A. x= 5"
The excluded values are x = 4 and x - 1
<h3>How to determine the excluded values?</h3>The complete question is added as an attachment
The function is given as:
(2x^2 - 7x - 4)/(x^2 - 5x + 4)
Set the denominator to 0
x^2 - 5x + 4 = 0
Expand
x^2 - x - 4x + 4 = 0
Factorize the equation
x(x -1) - 4(x - 1) = 0
This gives
(x - 4)(x - 1) = 0
Solve for x
x = 4 and x - 1
Hence, the excluded values are x = 4 and x - 1
Read more about excluded values at
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