Question

Solve x2 – 7x = –13.

Answer 1

This results in a non-real solution X= 7/2 + i (sqrt 3)/2 and x= 7/2 - i (sqrt 3)/2

Answer 2

we have

$x^{2} -7x=-13$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} -7x+3.5^{2}=-13+3.5^{2}$

$x^{2} -7x+12.25=-13+12.25$

$x^{2} -7x+12.25=-0.75$

Rewrite as perfect squares

$(x-3.5)^{2}=-0.75$

remember that

$i=\sqrt{-1}$

Square root both sides

$(x-3.5)=(+/-)\sqrt{-0.75}$

$(x-3.5)=(+/-)\sqrt{-1*0.75}$

$(x-3.5)=(+/-)\sqrt{0.75}i$

$x1=3.5+\sqrt{0.75}i$

$x2=3.5-\sqrt{0.75}i$

Simplify

$\sqrt{0.75}=\frac{\sqrt{3}}{2}$

$x1=3.5+\frac{\sqrt{3}}{2}i$

$x2=3.5-\frac{\sqrt{3}}{2}i$

therefore

the answer is

$x1=3.5+\frac{\sqrt{3}}{2}i$

$x2=3.5-\frac{\sqrt{3}}{2}i$