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

1 answer

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.