Question

Find the solution set for 8x^-9x=-1

Answer 1

`\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}`

`x=(1)/(8),\:x=1`

Explanation:

Given the equation

`8x^2-9x=-1\:\:`

Add 1 to both sides

`8x^2-9x+1=-1+1`

`8x^2-9x+1=0`

as

`\left(8x-1\right)\left(x-1\right)=8x^2-9x+1`

so the equation becomes

`\left(8x-1\right)\left(x-1\right)=0`

Using the zero factor principle:

`\:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)`

so

`8x-1=0\quad \mathrm{or}\quad \:x-1=0`

solving

`8x-1=0`

`8x=1`

`(8x)/(8)=(1)/(8)`

`x=(1)/(8)`

also solving

`x-1=0`

`x=1`

`\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}`

`x=(1)/(8),\:x=1`