Quadratic Equations Online Practice

Question

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Question
Solve the following quadratic equation using the perfect square trinomial pattern: 49x2=−392x−784
.(1 point)
Responses

x=784
x equals 784

x=−4
x equals negative 4

x=4
x equals 4

x=−784
x equals negative 784
Remaining Attempts : 3
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Answer 1

To solve the quadratic equation \( 49x^2 + 392x + 784 = 0 \) using the perfect square trinomial pattern, we first rewrite it in standard form.

1. Rewrite the equation: \[ 49x^2 + 392x + 784 = 0 \]

2. Factor out the common factor (49) from the left side: \[ 49(x^2 + 8x + 16) = 0 \] \[ 49(x + 4)^2 = 0 \]

3. Set the squared term equal to zero: \[ (x + 4)^2 = 0 \]

4. Solve for \( x \): \[ x + 4 = 0 \] \[ x = -4 \]

So, the correct solution is: x = -4.