Question

100 points PLEASE ANSWER
ASAP thank you so much
Please show work

Answer 1

The mistake is that the equation on both sides is multiplied by 8. Both sides should be divided by 8.

Explanation:

`8x^2-x-1=0`

`8x^2-x=1` Divide both sides of the equation by 8

`x^2-(1)/(8) x=(1)/(8)`

`x^2-(1)/(8) x+?=(1)/(8) +?` Add the same value to both side

`x^2-(1)/(8) x+(1)/(256) =(1)/(8) +(1)/(256)`
Use
`a^2-2ab+b^2=(a-b)^2`

`(x-(1)/(16) )^2 = (33)/(256)`

`x-(1)/(16)=+-(√(33) )/(16)`

`x_(1) =(-√(33)+1 )/(16)`

`x_(2) =(√(33)+1 )/(16)`

Answer 2

`x=(1 \pm √(33))/(16)`

Explanation:

Given:

`8x^2-x-1=0`

Add 1 to both sides:

`\implies 8x^2-x=1`

Factor out the 8 from the left side:

`\implies 8\left(x^2-(1)/(8)x\right)=1`

Divide both sides by 8:

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

Add the square of half the coefficient of x to both sides:

`\implies x^2-(1)/(8)x+(1)/(256)=(1)/(8)+(1)/(256)`

Factor the left side and simplifyy the right:

`\implies \left(x-(1)/(16)\right)^2=(33)/(256)`

Square root both sides:

`\implies x-(1)/(16)=\pm\sqrt{(33)/(256)}`

Simplify:

`\implies x-(1)/(16)=\pm(√(33))/(16)`

Add 1/16 to both sides:

`\implies x=\pm(√(33))/(16)+(1)/(16)`

Simplify:

`\implies x=(1 \pm √(33))/(16)`