Question
What is the intermediate step in the form as a result of completing the square
for the following equation?

Answer Attempt 1 out of 2

Ask by Newton Robbins. in the United States

Mar 26,2025

Question

Question What is the intermediate step in the form $$ (x+a)^{2}=b $$ as a result of completing the square for the following equation? $$ x^{2}-15 x+119=5 x-6 $$ Answer Attempt 1 out of 2

UpStudy AI · Accepted Answer

Rearrange the equation to bring all terms to one side:
$$
x^{2} - 15x + 119 = 5x - 6 \quad \Longrightarrow \quad x^{2} - 15x - 5x + 119 + 6 = 0,
$$
which simplifies to:
$$
x^{2} - 20x + 125 = 0.
$$

Next, move the constant term to the right-hand side:
$$
x^{2} - 20x = -125.
$$

To complete the square, take half of the coefficient of $$ x $$: 
$$
\frac{-20}{2} = -10, 
$$
and square it:
$$
(-10)^2 = 100.
$$

Add $$ 100 $$ to both sides:
$$
x^{2} - 20x + 100 = -125 + 100.
$$

The left-hand side becomes a perfect square:
$$
(x - 10)^2 = -25.
$$

Thus, the intermediate step is:
$$
(x - 10)^2 = -25.
$$
The intermediate step after completing the square is $$ (x - 10)^2 = -25 $$.

Question
What is the intermediate step in the form as a result of completing the square
for the following equation?

Answer Attempt 1 out of 2

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Question What is the intermediate step in the form as a result of completing the square for the following equation? Answer Attempt 1 out of 2