Question

Find the roots of the equation
x^2 +7= 2x
express your answer in simplest a +bi form

Answer 1

`x^2+7=2x\\\\\implies x^2 -2x +7 =0\\\\\text{Apply quadratic formula,}~ x =(-b \pm √(b^2-4ac))/(2a)\\\\\text{in this case,}~ a = 1, b= -2 ~\text{and}~ c = 7\\\\\\x= (-(-2) \pm √((-2)^2 -4\cdot 1 \cdot 7))/(2\cdot 1)\\\\\\\implies x =(2 \pm √(-24))/(2)\\\\\\\implies x = \frac{2 \pm i√(24)}2\\\\\implies x =\frac{2 \pm i2√(6)}2\\\\\implies x = \frac{2\left(1 \pm i \sqrt 6\right)}2\\\\\implies x = 1 \pm i\sqrt 6\\\\`

`\text{Hence,}~ x = 1-i\sqrt 6 ~\text{or}~ x = 1+i\sqrt 6`