SOLUTION: (x+6)^(1/2)=(x-9)

Question 214785: (x+6)^(1/2)=(x-9)

Found 2 solutions by drj, RAY100:
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!

Step 1. Square both sides of the equation

Step 2. Subtract x+6 from both sides of the equation to get a quadratic one.

Step 3. We can use the quadratic formula to solve this given as

where a=1, b=-19 and c=75

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=61 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 13.4051248379533, 5.59487516204667. Here's your graph:

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Step 2.
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
( x+6)^1/2 = (x-9),,,,,,square both sides
.
(x+6) = (x^2 -18x +81)
.
0 = x^2 -19x +75,,,,solve by quadratic formula
.
a=1,,,,b=-19,,,,,c=75
.
x=[ -(-19) +/- sqrt{ (-19)^2 - 4 (1)(75)} ] /2(1)
.
x=[ 19 +/- sqrt{ 361 - -300)}] 2
.
x= [ 19 +/- 7.810] /2
.
x= 13.405,,5.595
.
.
check,,,(5.595),,,,,,( 5.595 +6)^1/2 = 5.595 -9 = -3.405
.
+/-3.405 =-3.405,,,,ok
.
(13.405),,,,,,(13.405 +6)^1/2 = 13.405 -9 = 4.405
.
+/- 4.405 = 4.405,,,,,,,,ok
.

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