Answer:
\(16x^2+49=(x-\frac{7i}{4})(x+\frac{7i}{4})\)
Step-by-step explanation:
Given : Expression \(16x^2+49\)
To find : Factor the expression ?
Solution :
The given expression is a quadratic function \(y=ax^2+bx+c\) the solution is \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
On comparing with general form,
a=16, b=0, c=49
Substitute in the formula,
\(x=\frac{-0\pm\sqrt{0^2-4(16)(49)}}{2(16)}\)
\(x=\frac{\pm\sqrt{-3136}}{32}\)
\(x=\frac{\pm56i}{32}\)
\(x=\frac{56i}{32},\frac{-56i}{32}\)
\(x=\frac{7i}{4},\frac{-7i}{4}\)
Factors are \((x-\frac{7i}{4}),(x+\frac{7i}{4})\)
Therefore, \(16x^2+49=(x-\frac{7i}{4})(x+\frac{7i}{4})\)
