Question

Solve for x in the equation x² - 4x-9 = 29.a) X= 2+/- sqrt42b) X= 2+/- sqrt33c) X= 2+/- sqrt34d) X= 4+/- sqrt42

Answer 1

`x=2\pm\sqrt[]{42}\text{ (option A)}`

Step-by-step explanation:

x² - 4x - 9 = 29

Collect like terms:

x² - 4x - 9 - 29 = 0

x² - 4x - 38 = 0

For a quadratic equation: ax² + bx + c

a = 1 , b = -4, c = -38

We apply almighty formula to find the values of x

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`
`\begin{gathered} x\text{ = }\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(-38)}}{2(1)} \\ x\text{ =}\frac{4\pm\sqrt[]{16+152}}{2} \end{gathered}`
`\begin{gathered} x\text{ =}\frac{4\pm\sqrt[]{168}}{2}=\frac{4\pm\sqrt[]{4*42}}{2} \\ =\text{ }\frac{4\pm2\sqrt[]{42}}{2}=\frac{2(2\pm\sqrt[]{42)}}{2}=(2\pm\sqrt[]{42)} \\ x\text{ = 2 +}\sqrt[]{42\text{ }}\text{ or 2 -}\sqrt[]{42\text{ }} \end{gathered}`

The correct option: x= 2+/- sqrt42 (option A)