Answer :
Answer: x = 3
Step-by-step explanation:
I guess that the equation is:
(45 - 3x)^1/2 = x - 9
so let's solve it for x.
first, we can square both sides:
(45 - 3x) = (x - 9)^2 = x^2 - 18x + 81
now we can write this as a quadratic equation:
x^2 - 18x + 81 - 45 + 3x = 0
x^2 -15x + 36 = 0
now we can use the Bhaskara's equation to find the solutions for that equation:
where for a equation a*x^2 + b*x + c = 0
the solutions are:
[tex]x = \frac{-b +- \sqrt[2]{b^2 -4ac} }{2a}[/tex]
here a = 1, b = -15 and c = 36
[tex]x = \frac{15 +- \sqrt[2]{15^2 -4*36} }{2} = \frac{15+- 9}{2}[/tex]
then the solutions are:
x = (15 + 9)/2 = 24/2 = 12
x = (15 - 9)/2 = 6/2 = 3
where 12 is the solution for the positive (45 - 3x)^1/2 and x = 3 is the extraneous solution (because it works for the negative (45 - 3x)^1/2)