Answer:
x = 3 and 7
There are two true solutions.
Step-by-step explanation:
To solve [tex]x-7 = \sqrt{-4x+28}[/tex], use inverse operations by squaring both sides of the equal sign.
[tex](x-7)^2 = (\sqrt{-4x+28})^2\\x^2-14x+49 = -4x+28\\x^2-14x+4x+49-28 = 0\\x^2-10x+21=0[/tex]
The quadratic expression can be factored into binomials and set equal to 0 by the zero product property to find x.
(x - 3) ( x - 7) = 0
x-3 = 0 so x=3
x-7 = 0 so x=7
Now check each solution into the original equation to be sure it solve the solution and is not extraneous.
[tex]7-7 = \sqrt{-4(7)+28}\\ 0=0[/tex]
and
[tex]3-7 = \sqrt{-4(3)+28}\\[tex]-4 = \sqrt{16}\\-4 =-4[/tex][/tex]
Answer:
B. There are two true solutions
Step-by-step explanation:
(the two solutions would be x=3 and x=7)
