Question

I need help with this question please I’ll mark as brainliest

Answer 1

Answer:

$x=\frac{3}{2}+i\frac{\sqrt{23}}{2},\:x=\frac{3}{2}-i\frac{\sqrt{23}}{2}$

Step-by-step explanation:

$x^2-3x=-8$

$x^2-3x+8=-8+8$

$x^2-3x+8=0$

$\frac{-\left(-3\right)+\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:8}}{2\cdot \:1}$

$=\frac{3+\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:8}}{2\cdot \:1}$

$\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:8}$

$=\sqrt{-23}$

$=\sqrt{23}i$

$=\frac{3+\sqrt{23}i}{2}$

$=\frac{3}{2}+\frac{\sqrt{23}}{2}$

$\frac{-\left(-3\right)-\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:8}}{2\cdot \:1}$

$=\frac{3-\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:8}}{2\cdot \:1}$

$3-\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:8}$

$=\sqrt{-23}$

$=\sqrt{23}i$

$=3-\sqrt{23}i$

$=\frac{3-\sqrt{23}i}{2}$

$=\frac{3}{2}-\frac{\sqrt{23}}{2}i$

$x=\frac{3}{2}+i\frac{\sqrt{23}}{2},\:x=\frac{3}{2}-i\frac{\sqrt{23}}{2}$