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

Question

asked Feb 3, 2022 205k views

1 Answer

Leontalbot · Answer 1 · 2022-02-08T22:39:24+0000

Answer:

$x = (70 + √(900) )/(50)\\$ 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!