How do you solve sqrt (100 - d^2) = 10 - d√100−d2=10−d?

2 Answers
Konstantinos Michailidis
May 31, 2018

We have 10-d>=010−d≥0 or 10>=d10≥d

Hence

sqrt(100-d^2)=10-d√100−d2=10−d

sqrt((10+d)(10-d))=sqrt((10-d)^2)√(10+d)(10−d)=√(10−d)2

For d!=10d≠10 we have that

sqrt((10+d)/(10-d))=1√10+d10−d=1

Take squares in both sides

(10+d)/(10-d)=110+d10−d=1

10+d=10-d10+d=10−d

d=0d=0

Hence the solutions are d=0d=0 and d=10d=10

Shantelle
Jun 1, 2018

d = 0d=0 and 1010

Explanation:

sqrt(100-d^2) = 10 - d√100−d2=10−d

First, square both sides:
(sqrt(100-d^2))^2 = (10 - d)^2(√100−d2)2=(10−d)2

100 - d^2 = 100 - 20d + d^2100−d2=100−20d+d2

Subtract color(blue)100100 from both sides of the equation:
100 - d^2 quadcolor(blue)(-quad100) = 100 - 20d + d^2 quadcolor(blue)(-quad100)

-d^2 = -20d + d^2

Add color(blue)(d^2) to both sides of the equation:
-d^2 quadcolor(blue)(+quadd^2) = -20d + d^2 quadcolor(blue)(+quadd^2)

0 = 2d^2 -20d

Factor out a color(blue)(2d):
0 = 2d(d-10)

2d = 0 and d - 10 = 0

d = 0 and d = 10

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Now plug in both solutions to make sure they are really solutions:

First plug in 0:
sqrt(100-d^2) = 10 - d

sqrt(100-0) = 10 - 0

sqrt(100) = 10

10 = 10

This is true. Therefore, 0 is a solution.

Now plug in 10:
sqrt(100-d^2) = 10 - d

sqrt(100-10^2) = 10 - 10

sqrt(100-100)=0

sqrt0=0

0=0

This is also a solution.

Hope this helps!

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