Question

Solve the radical equation the square root of 8x+9=x+2, how would you start it?

Answer 1

Answer:  I will start it by squaring both sides of the equation.  

The solution is  x = 5 or x=-1

Step-by-step explanation:

$\sqrt{8x+9} =x+2$     Square the left and right sides. The square root of 8x+9 squared is 8x+9  and the x+2 squared is x^2 + 4x +4. We will now have the new equation,

8x + 9 = $x^{2}$ + 4x + 4   now set them equal zero first sutract x^2 from both sides

-x^2       -x^2

-x^2 + 8x + 9 = 4x +4      subtract 4x from both sides      

          -4x            -4x

-x^2 +4x + 9 = 4        Finally subtract 4 from both sides

               -4    -4

-x^2 + 4x +5 = 0    Remember the largest degree has a negative coefficient so divide them all by -1.

x^2 - 4x -5 = 0        Now find two numbers that their product is -5 and their sum is -4.     the numbers  1 and -5 works out.

Now rewrite the whole equation as,

x^2+ 1x -5x -5=0      Factor by grouping on the left side

x(x+1) -5(x+1)= 0      Factor out x+1

(x+1)(x-5) = 0         Now apply the zero product

x+1 = 0     or x-5 = 0

   -1    -1          +5   +5

x = -1   or  x = 5