Question
Solving Quadratic Equations Using Patterns Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
Solve the following quadratic equation using the perfect square trinomial pattern: x2+54x=−729
.(1 point)
x=
Remaining Attempts : 3
Skip to navigation
Answers
GPT-4o mini
To solve the quadratic equation \( x^2 + 54x = -729 \) using the perfect square trinomial pattern, we first want to move all terms to one side of the equation:
\[
x^2 + 54x + 729 = 0
\]
Next, we will complete the square. The goal is to rewrite the left side as a perfect square trinomial. A perfect square trinomial has the form \( (x + a)^2 \).
1. Take half of the coefficient of \( x \), which is \( 54 \), and square it:
\[
\left(\frac{54}{2}\right)^2 = 27^2 = 729
\]
2. Therefore, we can rewrite the left side:
\[
x^2 + 54x + 729 = (x + 27)^2
\]
Now we set the equation equal to zero:
\[
(x + 27)^2 = 0
\]
3. To solve for \( x \), take the square root of both sides:
\[
x + 27 = 0
\]
4. Finally, solve for \( x \):
\[
x = -27
\]
Thus, the solution to the equation \( x^2 + 54x = -729 \) is:
\[
\boxed{-27}
\]
\[
x^2 + 54x + 729 = 0
\]
Next, we will complete the square. The goal is to rewrite the left side as a perfect square trinomial. A perfect square trinomial has the form \( (x + a)^2 \).
1. Take half of the coefficient of \( x \), which is \( 54 \), and square it:
\[
\left(\frac{54}{2}\right)^2 = 27^2 = 729
\]
2. Therefore, we can rewrite the left side:
\[
x^2 + 54x + 729 = (x + 27)^2
\]
Now we set the equation equal to zero:
\[
(x + 27)^2 = 0
\]
3. To solve for \( x \), take the square root of both sides:
\[
x + 27 = 0
\]
4. Finally, solve for \( x \):
\[
x = -27
\]
Thus, the solution to the equation \( x^2 + 54x = -729 \) is:
\[
\boxed{-27}
\]
Related Questions
Solving Quadratic Equations Using Patterns Practice
Complete this assessment to review what you’v...
Solving Quadratic Equations Using Patterns Practice
Complete this assessment to review what you’ve...
Solving Quadratic Equations Using Patterns Practice
Complete this assessment to review what you’v...
Solving Quadratic Equations Using Patterns Practice
Complete this assessment to review what you’v...