Question

Solve the radical equation x – 7 = square root of -4x+28. Which statement is true about the solutions to the radical equation? There are no true solutions. There are two true solutions. There is one extraneous solution, with a value greater than 4. There is one true solution, with a value greater than 6.

Answer 1

Answer:

x = 3 and 7

There are two true solutions.

Step-by-step explanation:

To solve $x-7 = \sqrt{-4x+28}$, use inverse operations by squaring both sides of the equal sign.

$(x-7)^2 = (\sqrt{-4x+28})^2\\x^2-14x+49 = -4x+28\\x^2-14x+4x+49-28 = 0\\x^2-10x+21=0$

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.

$7-7 = \sqrt{-4(7)+28}\\ 0=0$

and

$3-7 = \sqrt{-4(3)+28}\\[tex]-4 = \sqrt{16}\\-4 =-4$[/tex]