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

Explanation:

`√(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