Solve x 2 - 4x - 7 = 0 by completing the square. What are the solutions?
1 answer:
Answer:
x = 2±sqrt(11)
Step-by-step explanation:
x^2 -4x - 7 =0
Add 7 to each side
x^2 -4x -7+7 =0+7
x^2 -4x =7
To complete the square take the coefficient of the x term and divide by 2 and then square it. Add it to both sides
-4 /2 = -2 then square
(-2)^2 = 4
Add 4 to both sides
x^2 -4x+4 =7+4
x^2 -4x+4 = 11
Factor the left side into (x-b/2)^2
(x-2)^2 =11
Take the square root of each side
sqrt((x-2)^2) =±sqrt(11)
x-2 = ±sqrt(11)
Add to to each side
x-2+2 = 2±sqrt(11)
x = 2±sqrt(11)
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The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs:
The hypotenuse is the side with the greatest length.
Check all options:
1. c=5, a=3, b=4:
true.
2. c=14, a=4, b=11:
false.
3. c=17, a=9, b=14:
false.
4. c=16, a=8, b=14:
false.
5. c=17, a=8, b=15:
true.
Answer: correct options are A and E.
Answer:
B. and D.
B. 10m+3m+m+10+6=4m+16
D. 4(m+4)=4m+16
The answer is X=19/2 y=10
215 - 44.49 (I added the two deductions mentally) = 170.51
I see the percentages 2%, 1% and 3% add up to 6%
So we want 6% of 215 or .06 x 215 = $12.90
$170.51 - 12.90 = $157.61 net income.
