Question

solve for x.
5x² + 70x + 245 = 0
x =

Explanation:

Step1: Simplify the equation

First, we can divide the entire equation by 5 to simplify it.
$$\frac{5x^{2}+70x + 245}{5}=\frac{0}{5}$$
Which simplifies to:
$$x^{2}+14x + 49 = 0$$

Step2: Factor the quadratic equation

Notice that the quadratic is a perfect square trinomial. The form of a perfect square trinomial is \(a^{2}+2ab + b^{2}=(a + b)^{2}\). Here, \(a=x\) and \(b = 7\) (since \(2ab=2\times x\times7 = 14x\) and \(b^{2}=49\)). So we can factor the equation as:
$$(x + 7)^{2}=0$$

Step3: Solve for \(x\)

Taking the square root of both sides, we get:
$$x+7=0$$
Subtracting 7 from both sides gives:
$$x=-7$$

Answer:

\(-7\)