Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Complete the square to solve the following quadratic equation: x2−22x+1=15 .(1 point) Responses x=−11+14−−√, −11−14−−√ x equals...Asked by HaydenReturned
Complete the square to solve the following quadratic equation: x2−22x+1=15
.(1 point)
Responses
x=−11+315−−√, −11−315−−√
x equals negative 11 plus 3 Start Root 15 End Root comma negative 11 minus 3 Start Root 15 End Root
x=−11+14−−√, −11−14−−√
x equals negative 11 plus Start Root 14 End Root comma negative 11 minus Start Root 14 End Root
x=11+315−−√, 11−315−−√
x equals 11 plus 3 Start Root 15 End Root comma 11 minus 3 Start Root 15 End Root
x=11+14−−√, 11−14−−√
.(1 point)
Responses
x=−11+315−−√, −11−315−−√
x equals negative 11 plus 3 Start Root 15 End Root comma negative 11 minus 3 Start Root 15 End Root
x=−11+14−−√, −11−14−−√
x equals negative 11 plus Start Root 14 End Root comma negative 11 minus Start Root 14 End Root
x=11+315−−√, 11−315−−√
x equals 11 plus 3 Start Root 15 End Root comma 11 minus 3 Start Root 15 End Root
x=11+14−−√, 11−14−−√
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the quadratic equation \( x^2 - 22x + 1 = 15 \) by completing the square, we first rearrange the equation:
\[
x^2 - 22x + 1 - 15 = 0
\]
This simplifies to:
\[
x^2 - 22x - 14 = 0
\]
Now, we'll complete the square for the expression \( x^2 - 22x \).
1. Take half of the coefficient of \( x \) (which is -22), square it, and add it to both sides:
Half of -22 is -11, and squaring -11 gives \( 121 \).
2. Rewrite the equation by adding \( 121 \) to both sides:
\[
x^2 - 22x + 121 = 14 + 121
\]
This simplifies to:
\[
(x - 11)^2 = 135
\]
3. Now take the square root of both sides:
\[
x - 11 = \pm \sqrt{135}
\]
4. Finally, solve for \( x \):
\[
x = 11 \pm \sqrt{135}
\]
Now let's simplify \( \sqrt{135} \):
\[
\sqrt{135} = \sqrt{9 \times 15} = 3\sqrt{15}
\]
So, we have:
\[
x = 11 \pm 3\sqrt{15}
\]
Thus, the solutions are:
\[
x = 11 + 3\sqrt{15}, \quad 11 - 3\sqrt{15}
\]
The correct response from the options provided is:
**x = 11 + 3√15, 11 - 3√15**.
\[
x^2 - 22x + 1 - 15 = 0
\]
This simplifies to:
\[
x^2 - 22x - 14 = 0
\]
Now, we'll complete the square for the expression \( x^2 - 22x \).
1. Take half of the coefficient of \( x \) (which is -22), square it, and add it to both sides:
Half of -22 is -11, and squaring -11 gives \( 121 \).
2. Rewrite the equation by adding \( 121 \) to both sides:
\[
x^2 - 22x + 121 = 14 + 121
\]
This simplifies to:
\[
(x - 11)^2 = 135
\]
3. Now take the square root of both sides:
\[
x - 11 = \pm \sqrt{135}
\]
4. Finally, solve for \( x \):
\[
x = 11 \pm \sqrt{135}
\]
Now let's simplify \( \sqrt{135} \):
\[
\sqrt{135} = \sqrt{9 \times 15} = 3\sqrt{15}
\]
So, we have:
\[
x = 11 \pm 3\sqrt{15}
\]
Thus, the solutions are:
\[
x = 11 + 3\sqrt{15}, \quad 11 - 3\sqrt{15}
\]
The correct response from the options provided is:
**x = 11 + 3√15, 11 - 3√15**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.