Solve the following quadratic equation for all values of x in simplest form. 9, left parenthesis, 5, x, minus, 8, right parenthesis, squared, minus, 5, equals, minus, 1 9(5x−8) 2 −5= −1

Answer 1

To solve this quadratic equation, we first need to expand and simplify the left side of the equation:

9(5x - 8)^2 - 5 = -1
Expanding (5x - 8)^2, we get:
9(25x^2 - 80x + 64) - 5 = -1
Distribute the 9:
225x^2 - 720x + 576 - 5 = -1
Combine like terms:
225x^2 - 720x + 571 = -1
Add 1 to both sides:
225x^2 - 720x + 572 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 225, b = -720, and c = 572. To solve for x, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values of a, b, and c:
x = (720 ± √((-720)^2 - 4(225)(572))) / 2(225)
x = (720 ± √(518400 - 514800)) / 450
x = (720 ± √3600) / 450

Now, we simplify:
x = (720 ± 60) / 450

The two solutions are:
x = (720 + 60) / 450 = 780 / 450 = 13/15
x = (720 - 60) / 450 = 660 / 450 = 22/15

Therefore, the solutions to the quadratic equation are x = 13/15 and x = 22/15.