Question

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

Answer 1

`x=2+i√(11)`

`x=2-i√(11)`

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(+/-)√(16-60)} {2}`

Remember that

`i=√(-1)`

`x=\frac{4(+/-)√(-44)} {2}`

`x=\frac{4(+/-)2i√(11)} {2}`

`x=(4(+)2i√(11))/(2)=2+i√(11)`

`x=(4(-)2i√(11))/(2)=2-i√(11)`