Answer: I will start it by squaring both sides of the equation.
The solution is x = 5 or x=-1
Step-by-step explanation:
[tex]\sqrt{8x+9} =x+2[/tex] 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 = [tex]x^{2}[/tex] + 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
