SOLUTION: Can you please solve this equation: sqrt( x + 5) = sqrt(x^2 - 15)

Algebra.Com
Question 246169: Can you please solve this equation:
sqrt( x + 5) = sqrt(x^2 - 15)
Found 2 solutions by unlockmath, richwmiller:
Answer by unlockmath(1688)   (Show Source): You can put this solution on YOUR website!
Hello,
If we square each side then the square roots cancel.
[sqrt( x + 5)]^2 = [sqrt(x^2 - 15)]^2 reults in:
x + 5 = x^2 - 15 Now move the x + 5 to the other side:
0=x^2-x-20 Now we can factor this to be:
0= (x-5)(x+4)This gives us:
x=5
x=-4
These can be put into the original problem.
Does it work out?
RJ Toftness
Check out my book at www.math-unlock.com
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
sqrt( x + 5) = sqrt(x^2 - 15)
square both sides
x+5=x^2-15
subtract x+5
0=x^2-x-10
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=41 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.70156211871642, -2.70156211871642. Here's your graph:

we can also solve by completing the square
add 10 to both sides
10=x^2-x
add (1/2)^2 to both sides
41/4=x^2-x+1/4
factor
41/4=(x-1/2)^2
get sqrt
sqrt(41)/2=x-1/2
-sqrt(41)/2=x-1/2
add 1/2 to both sides
1/2-sqrt(41)/2=x
1/2+sqrt(41)/2=x
factor
1/2(1-sqrt(41))=x
1/2(1+sqrt(41))=x


RELATED QUESTIONS

multiply sqrt (5) + sqrt (3) x sqrt (5) - sqrt (3). please help solve this equation.... (answered by jim_thompson5910,Alan3354)
can you sole this please: sqrt X+4 - sqrt X-1 = 2/sqrt... (answered by mananth)
Please help me solve this equation {{{sqrt(3x-5)=7-sqrt(x +... (answered by scott8148)
Please help me solve this equation... (answered by jim_thompson5910)
Solve. a) {{{5 + sqrt ( x ) = 15}}} b) {{{2}}}{{{ sqrt ( x+1 ) = sqrt ( x-5 )}}} Can (answered by Fombitz)
Please help me solve this equation: {{{... (answered by ewatrrr)
solve sqrt x + 5 = sqrt x^2 -... (answered by rapaljer)
Please help me solve this equation: {{{ sqrt (sqrt (x+5) +x) = 5... (answered by josgarithmetic,ikleyn)
Can you please help me solve this question (4 sqrt x)(4 sqrt x) = ? (answered by rothauserc)