$16 x^{2}+56 x+49=0$

Step 1 ：Given the quadratic equation \(16x^{2}+56x+49=0\)

Step 2 ：This is a quadratic equation of the form \(ax^{2}+bx+c=0\). The solutions to this equation can be found using the quadratic formula \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Here, \(a=16\), \(b=56\), and \(c=49\)

Step 3 ：Substitute \(a=16\), \(b=56\), and \(c=49\) into the discriminant formula \(D=b^{2}-4ac\) to get \(D=0\)

Step 4 ：Substitute \(a=16\), \(b=56\), and \(D=0\) into the quadratic formula to get \(x1 = -1.75\) and \(x2 = -1.75\)

Step 5 ：Since the discriminant is zero, the equation has only one distinct real root

Step 6 ：Therefore, the final answer is \(x = -1.75\)

Step 7 ：Final Answer: \(\boxed{-1.75}\)