Question

study the steps shown to solve the given equation.
\\(\sqrt{30 - 2x} = x - 3\\)
\\(30 - 2x = x^2 - 6x + 9\\)
\\(0 = x^2 - 4x - 21\\)
\\(0 = (x + 3)(x - 7)\\)
based on the above work, possible solutions of the equation are dropdown.

Explanation:

Find the roots of the factored equation

Using the Zero Product Property knowledge point

$$
LATEXBLOCK0
$$

Check for extraneous solutions

Using the Solving Radical Equations and Extraneous Solutions knowledge points

$$
LATEXBLOCK1
$$

Determine the possible solutions based on the steps

The algebraic steps shown lead to the factored equation \(0 = (x + 3)(x - 7)\). Based strictly on the algebraic work shown up to that point, the possible solutions (before checking for extraneous solutions) are \(x = -3\) and \(x = 7\).

Answer:

Study the steps shown to solve the given equation.

$$\sqrt{30-2x} = x-3$$

$$30-2x = x^2-6x+9$$

$$0 = x^2-4x-21$$

$$0 = (x+3)(x-7)$$

Based on the above work, possible solutions of the equation are <blank>\(x = -3\) and \(x = 7\)</blank>.