Solve the equation for x. if a solution is extraneous, be sure to identify it on your final answer.
square root x + 6 - 4 = x

The solutions to the equation are x = -5 or x = -2.

We first isolate the square root.  To do this, we cancel the 4 by adding it to each side:

Next we want to cancel the square root sign.  To do this, we square both sides of the equation:

Now we want to gather all of the variables on one side of the equation.  The simplest way to do this will be to subtract x from each side:

To solve quadratic equations (those with an x² term), we want ot set them equal to 0.  To do this, we subtract 6 from each side:

We can now factor the right hand side of the equation.  To do this, we find factors of the constant, 10, that sum to the x term, 7.  Looking at all of the factors of 10, we see that 5 and 2 have a sum of 7; this gives us

Using the zero product property, we know that in order to have a product of 0, one or more of the factors must be equal to 0.  This tells us that we have

To solve the first equation, we subtract 5 from each side:

To solve the second equation, we subtract 2 from each side:

This means the solutions are x = -5 or x = -2.

Learn more about quadratic equations at:  

Learn more about factoring at:  

Learn more about radical equations at:  

Keywords:  radical equation, identify extraneous solution, square root equation

3/5

step-by-step explanation:

double number line is not a standard concept, so it must have been defined in your textbook. assume top line is numerator.

b). 4320 have a nice day