Question 845255: solve the equation for x. If neccesary, round your answer to two decimal places.
x+2=square root of 3x+16 Answer by pmesler(52) (Show Source):
You can put this solution on YOUR website! The equation says x+2 = sqrt(3x+16)
First, to solve for x we need to simplify the equation. To do that we need to eliminate the square root symbol. We do that by performing the opposite or inverse function. The inverse function of a square root is to square something. It's important to note that we need to do this for both sides of the equation.
Therefore our new equation is
(x+2)^2 = (sqrt(3x+16))^2
That gives us
(x+2)(x+2) = 3x+16
Use the FOIL method to simplify the left-hand side.
x^2+4x+4 = 3x+16
Right away we see that our equation is becoming a quadratic equation. Let's simplify the whole equation so we have a quadratic expression on the left side and a zero on the right side.
Let's subtract 3x from both sides to get
x^2 + x + 4 = 16
Now, let's get rid of the 16 so we're left with a zero on the right-hand side.
Subtract 16 from both sides.
x^2+x-12 = 0.
Now, we use the quadratic formula to solve for x.
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=49 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 3, -4.
Here's your graph:
The solutions are x = -4 and x = 3
Let's check our answers to see which of these roots is extraneous.
If we substitute x = -4 into the original equation we get this:
-4 + 2 = sqrt(3(-4) + 16)
-2 = sqrt(-12 + 16)
-2 = sqrt ( 4)
-2 = 2. This is obviously false, so x = -4 is an extraneous root. Let's check the other root, x = 3.
3+2 = sqrt(3(3) + 16).
5 = sqrt ( 9 + 15)
5 = sqrt ( 25 )
5 = 5. That checks out so the solution is x = 3.
