SOLUTION: Find all real or imaginary solutions to each equation. Us e the method of your choice. Sq rt of 7x+29 = x + 3

Question 98541: Find all real or imaginary solutions to each equation. Us e the method of your choice.
Sq rt of 7x+29 = x + 3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Square both sides

Foil

Get all terms to one side

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-1, and c=-20

Negate -1 to get 1

Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our possible solutions are:
or

Check:
Lets check the possible solution x=5
Start with the given equation

Plug in x=5

Multiply

Add

Take the square root of both sides

Since the equation is true, x=5 is a solution

------------------------------
Lets check the possible solution x=-4
Start with the given equation

Plug in x=-4

Multiply

Add

Take the square root of both sides

Since the equation is not true, x=-4 is not a solution

So our only solution is x=5
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