Question

X^2=4x-15 solve with Quadratic formula

Answer 1

Answer:

$x=2+i\sqrt{11}$

$x=2-i\sqrt{11}$

Step-by-step explanation:

we have

$x^{2} =4x-15$ -------> $x^{2}-4x+15=0$

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}-4x+15=0$

so

$a=1\\b=-4\\c=15$

substitute in the formula

$x=\frac{-(-4)(+/-)\sqrt{-4^{2}-4(1)(15)}} {2(1)}$

$x=\frac{4(+/-)\sqrt{16-60}} {2}$

Remember that

$i=\sqrt{-1}$

$x=\frac{4(+/-)\sqrt{-44}} {2}$

$x=\frac{4(+/-)2i\sqrt{11}} {2}$

$x=\frac{4(+)2i\sqrt{11}}{2}=2+i\sqrt{11}$

$x=\frac{4(-)2i\sqrt{11}}{2}=2-i\sqrt{11}$