Question

solve for x in the equation ( x^2 - 4x - 9 = 29 )
( x = 2 pm sqrt{42} )
( x = 2 pm sqrt{33} )
( x = 2 pm sqrt{34} )
( x = 4 pm sqrt{42} )

Explanation:

Step1: Rearrange equation to standard form

$x^2 - 4x - 9 - 29 = 0$
$x^2 - 4x - 38 = 0$

Step2: Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, $a=1$, $b=-4$, $c=-38$
$x=\frac{4\pm\sqrt{(-4)^2-4(1)(-38)}}{2(1)}$

Step3: Calculate discriminant

$\sqrt{16 + 152} = \sqrt{168} = \sqrt{4\times42} = 2\sqrt{42}$

Step4: Simplify the expression

$x=\frac{4\pm2\sqrt{42}}{2}=2\pm\sqrt{42}$

Answer:

$x=2\pm\sqrt{42}$ (corresponding to the first option)