Question

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

Answer 1

Answer:

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

Step-by-step explanation:

$8x^2-x-1=0$
$8x^2-x=1$   Divide both sides of the equation by 8
$x^2-\frac{1}{8} x=\frac{1}{8}$
$x^2-\frac{1}{8} x+?=\frac{1}{8} +?$ Add the same value to both side
$x^2-\frac{1}{8} x+\frac{1}{256} =\frac{1}{8} +\frac{1}{256}$              
Use $a^2-2ab+b^2=(a-b)^2$
$(x-\frac{1}{16} )^2 = \frac{33}{256}$
$x-\frac{1}{16}=+-\frac{\sqrt{33} }{16}$
$x_{1} =\frac{-\sqrt{33}+1 }{16}$
$x_{2} =\frac{\sqrt{33}+1 }{16}$

Answer 2

Answer:

$x=\dfrac{1 \pm \sqrt{33}}{16}$

Step-by-step 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:

$\implies 8\left(x^2-\dfrac{1}{8}x\right)=1$

Divide both sides by 8:

$\implies x^2-\dfrac{1}{8}x=\dfrac{1}{8}$

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

$\implies x^2-\dfrac{1}{8}x+\dfrac{1}{256}=\dfrac{1}{8}+\dfrac{1}{256}$

Factor the left side and simplifyy the right:

$\implies \left(x-\dfrac{1}{16}\right)^2=\dfrac{33}{256}$

Square root both sides:

$\implies x-\dfrac{1}{16}=\pm\sqrt{\dfrac{33}{256}}$

Simplify:

$\implies x-\dfrac{1}{16}=\pm\dfrac{\sqrt{33}}{16}$

Add 1/16 to both sides:

$\implies x=\pm\dfrac{\sqrt{33}}{16}+\dfrac{1}{16}$

Simplify:

$\implies x=\dfrac{1 \pm \sqrt{33}}{16}$