To solve the quadratic equation 49x^2 = -392x - 784 using the perfect square trinomial pattern, we need to first rewrite the equation in the form (x + p)^2 = q.
We can start by dividing the entire equation by 49 to make the coefficient of x^2 equal to 1:
x^2 = -392/49x - 784/49
Next, we rewrite the middle term (-392/49x) as (-2x * 14/1):
x^2 = -2x * 14/1 - 784/49
Now, we can rewrite the equation as a perfect square trinomial:
x^2 + 2 * 14/1 * x + (14/1)^2 = (784/49) + (14/1)^2
Simplifying:
x^2 + 28x + 196 = 784/49 + 196
x^2 + 28x + 196 = 784/49 + 196/1
x^2 + 28x + 196 = (784 + 196 * 49) / 49
x^2 + 28x + 196 = (784 + 9604) / 49
x^2 + 28x + 196 = 10388 / 49
Now, we can simplify the right side of the equation:
x^2 + 28x + 196 = 212
Finally, we can solve for x by taking the square root of both sides:
x + 14 = ±√212
Simplifying:
x = -14 ± √212
Therefore, the solutions to the quadratic equation 49x^2 = -392x - 784 using the perfect square trinomial pattern are x = -14 + √212 and x = -14 - √212.
Solve the following quadratic equation using the perfect square trinomial pattern: 49x2=−392x−784 .
3 answers
Options for the problem are:
x=784
x=4
x=-784
x=-4
x=784
x=4
x=-784
x=-4
Apologies for the confusion. We will re-evaluate the quadratic equation and find the correct solutions.
The given equation is 49x^2 = -392x - 784.
To solve this quadratic equation using the perfect square trinomial pattern, we need to rewrite it in the form (x + p)^2 = q.
First, let's move all terms to one side of the equation to have a standard quadratic equation form:
49x^2 + 392x + 784 = 0
Now, let's factor out the common factor of 49 to simplify the equation:
49(x^2 + 8x + 16) = 0
Next, we recognize that the trinomial in the parentheses can be factored as a perfect square:
49(x + 4)^2 = 0
To find the solutions, we set each factor equal to zero:
x + 4 = 0
x = -4
Therefore, the correct solution to the quadratic equation 49x^2 = -392x - 784 using the perfect square trinomial pattern is x = -4.
The given equation is 49x^2 = -392x - 784.
To solve this quadratic equation using the perfect square trinomial pattern, we need to rewrite it in the form (x + p)^2 = q.
First, let's move all terms to one side of the equation to have a standard quadratic equation form:
49x^2 + 392x + 784 = 0
Now, let's factor out the common factor of 49 to simplify the equation:
49(x^2 + 8x + 16) = 0
Next, we recognize that the trinomial in the parentheses can be factored as a perfect square:
49(x + 4)^2 = 0
To find the solutions, we set each factor equal to zero:
x + 4 = 0
x = -4
Therefore, the correct solution to the quadratic equation 49x^2 = -392x - 784 using the perfect square trinomial pattern is x = -4.