Question

1. 4x - x² + 8 = 0

Explanation:

Step1: Rearrange to standard quadratic form

Rearrange terms to $ax^2+bx+c=0$:
$$x^2 - 4x - 8 = 0$$

Step2: Identify coefficients

Define $a, b, c$ for quadratic formula:
$a=1$, $b=-4$, $c=-8$

Step3: Apply quadratic formula

Use $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$:
$$x=\frac{4\pm\sqrt{(-4)^2-4(1)(-8)}}{2(1)}$$

Step4: Calculate discriminant

Compute value under square root:
$$\sqrt{16 + 32}=\sqrt{48}=4\sqrt{3}$$

Step5: Simplify the expression

Reduce the fraction:
$$x=\frac{4\pm4\sqrt{3}}{2}=2\pm2\sqrt{3}$$

Answer:

$x=2+2\sqrt{3}$ or $x=2-2\sqrt{3}$