Questions: Complete the square in the expression. Then factor the perfect square trinomial. x^2-21 x Complete the square. The expression is (Do not factor.) Factor the result. The factored expression is (Simplify your answer.)

Solution Steps

To complete the square for the expression \( x^2 - 21x \), we first rewrite it by adding and subtracting \( \left(\frac{-21}{2}\right)^2 \):

\[ x^2 - 21x = \left(x - \frac{21}{2}\right)^2 - \left(\frac{21}{2}\right)^2 \]

This simplifies to:

\[ x^2 - 21x = \left(x - 10.5\right)^2 - 110.25 \]

Thus, the completed square expression is:

\[ x(x - 21) \]

The expression can be factored as a perfect square trinomial:

\[ x^2 - 21x + 110.25 = 110.25\left(0.0952380952380952 x - 1.0\right)^{2} \]

This gives us the factored expression:

\[ 110.25\left(0.0952 x - 1.0\right)^{2} \]

Final Answer