Question

Giving 40 points!!! please help

Select the correct answer.
What are the solutions of this quadratic equation?
x²+4=8x+5
A.
x = 8 + √34
B.
* = 8 + 2√17
C.
x=4 ± √7
D. x=4 ± √17

Answer 1

`\textsf{D.} \quad x=4 \pm √(17)`

Explanation:

Rearrange the equation so it equals zero:

`\begin{aligned} x^2+4 & =8x+5 \\ \implies x^2+4-8x-5 & = 0\\x^2-8x-1&=0\end{aligned}`

Now use the quadratic formula to solve for x:

`x=(-b \pm √(b^2-4ac) )/(2a)\quad\textsf{when }\:ax^2+bx+c=0`

`a=1, \quad b=-8, \quad c=-1`

`\implies x=(-(-8) \pm √((-8)^2-4(1)(-1)))/(2(1))`

`\implies x=(8 \pm √(68))/(2)`

`\implies x=(8 \pm √(4\cdot 17))/(2)`

`\implies x=(8 \pm √(4)√(17))/(2)`

`\implies x=(8 \pm 2√(17))/(2)`

`\implies x=4 \pm √(17)`