Solve the following quadratic equation by factoring using the perfect square trinomial pattern: 4x2+20x=−25(1 point)Responsesx=−54x is equal to negative 5 fourthsx=52x is equal to 5 halvesx=−52x is equal to negative 5 halvesx=54

Answer 1

To solve the quadratic equation \(4x^2 + 20x = -25\) by factoring, we first rewrite the equation in standard form:

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

Next, we notice that this can be factored as a perfect square trinomial. We can rewrite the left side as:

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

Now, we solve for \(x\) by taking the square root of both sides:

\[ 2x + 5 = 0 \]

Subtracting 5 from both sides gives:

\[ 2x = -5 \]

Now, dividing by 2:

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

Thus, the solution to the equation is:

\[ \boxed{-\frac{5}{2}} \]