solve for x in the equation $x^{2}-4x - 9=29$.\n$x = 2pmsqrt{42}$\n$x = 2pmsqrt{33}$\n$x = 2pmsqrt{34}$\n$x…

Explanation:

Step1: Rearrange to standard quadratic form

$x^{2}-4x - 9-29 = 0$, so $x^{2}-4x - 38=0$.

Step2: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, here $a = 1$, $b=-4$, $c=-38$.

Step3: Use quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: $x=\frac{-(-4)\pm\sqrt{(-4)^{2}-4\times1\times(-38)}}{2\times1}$.

Step4: Simplify the expression

First, calculate inside the square - root: $(-4)^{2}-4\times1\times(-38)=16 + 152=168$. Then, $\sqrt{168}=\sqrt{4\times42}=2\sqrt{42}$. And $\frac{4\pm2\sqrt{42}}{2}=2\pm\sqrt{42}$.

Answer:

$x = 2\pm\sqrt{42}$