Question

Decide how many solutions the equation has. $$x^{2}-14 x+49=0$$

Short answer

The given equation has exactly one solution.

Step-by-step solution

Identify a, b, c

Firstly, we identify the coefficients a, b, and c from the equation. Here, a = 1, b = -14, and c = 49.

Calculate the Discriminant

Secondly, we calculate the discriminant using the formula \(b^{2} - 4ac\). Substitute the values of a and b into the formula, the calculation becomes :\((-14)^2 - 4*1*49 = 196 - 196 = 0\)

Determine the Number of Solutions

Lastly, we observe that the discriminant is 0, which indicates that the equation has exactly one real solution.