Question

(5x-7)^2-1=8 solve for x

Answer 1

`x = (70 + √(900) )/(50)\\` or
`x = 2`

Or:

`x = (70 - √(900) )/(50)\\` or
`x = (4)/(5)`

Explanation:

Step 1 - Simplify by expanding the brackets:

`(5x - 7)^2\\(5x - 7)(5x - 7)\\25x^2 - 35x - 35x + 49\\25x^2 - 70x + 49 - 1\\25x^2 - 70x + 48 = 8`

Step 2 - Subtract 8 from both sides so the equation equals 0:

`25x^2 - 70x + 48 - 8 = 8 - 8\\25x^2 - 70x + 40 = 0`

Step 3 - Use the quadratic formula:

`x = (-b +- √(b^2 - 4ac) )/(2a)\\a = 25\\b = -70\\c = 40`

Plug variables in:

`(-(-70) +- √((-70)^2 - (4 * 25 * 40)) )/(2 * 25)`

`(70 +- √(4900 - 4000) )/(50)\\\\(70 +- √(900) )/(50)\\`

So x is either:

`x = (70 + √(900) )/(50)\\`

`x = 2`

Or:

`x = (70 - √(900) )/(50)\\`

`x = (4)/(5)`

Hope this helps!