Question

solve for w, where w is a real number.
w = \sqrt{10w - 24}
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
w =

Explanation:

Step1: Square both sides to eliminate the square root.

Given \( w = \sqrt{10w - 24} \), squaring both sides gives \( w^2 = 10w - 24 \).

Step2: Rearrange into a quadratic equation.

Rearrange the equation to standard quadratic form: \( w^2 - 10w + 24 = 0 \).

Step3: Factor the quadratic equation.

Factor the quadratic: \( (w - 4)(w - 6) = 0 \).

Step4: Solve for w.

Set each factor equal to zero: \( w - 4 = 0 \) or \( w - 6 = 0 \), so \( w = 4 \) or \( w = 6 \).

Step5: Check for extraneous solutions.

• For \( w = 4 \): Substitute into the original equation: \( 4 = \sqrt{10(4) - 24} = \sqrt{40 - 24} = \sqrt{16} = 4 \). This is valid.
• For \( w = 6 \): Substitute into the original equation: \( 6 = \sqrt{10(6) - 24} = \sqrt{60 - 24} = \sqrt{36} = 6 \). This is valid.

Answer:

4, 6