Question

Solve the following quadratic equation by factoring using the perfect square trinomial pattern: 25x2−20x=−4 .(1 point) Responses x=25 x equals Start Fraction 2 over 5 End Fraction x=−25 x equals negative Start Fraction 2 over 5 End Fraction x=−45 x equals negative Start Fraction 4 over 5 End Fraction x=45

Answer 1

To solve the quadratic equation \( 25x^2 - 20x = -4 \) by factoring using the perfect square trinomial pattern, we first rearrange the equation:

\[
25x^2 - 20x + 4 = 0
\]

Now, we can rewrite the left side as a perfect square trinomial. Notice that:

\[
25x^2 - 20x + 4 = (5x - 2)^2
\]

Now the equation becomes:

\[
(5x - 2)^2 = 0
\]

To solve for \( x \), we take the square root of both sides:

\[
5x - 2 = 0
\]

Now we solve for \( x \):

\[
5x = 2
\]
\[
x = \frac{2}{5}
\]

So the solution to the quadratic equation is:

\[
x = \frac{2}{5}
\]

Thus, the correct response is:

**x equals Start Fraction 2 over 5 End Fraction.**