Explanation:
Of course, I can help you with this equation. Let's solve for x:
4x^2 - 64 = 8x - 4
First, move all the terms to one side of the equation to set it equal to zero:
4x^2 - 8x - 64 + 4 = 0
Now, combine like terms:
4x^2 - 8x - 60 = 0
Next, divide the entire equation by 4 to simplify it:
x^2 - 2x - 15 = 0
Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -2, and c = -15. To solve for x, you can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plug in the values:
x = (-(-2) ± √((-2)² - 4(1)(-15))) / (2(1))
x = (2 ± √(4 + 60)) / 2
x = (2 ± √64) / 2
Now, simplify:
x = (2 ± 8) / 2
Now, we have two possible solutions:
x = (2 + 8) / 2 = 10 / 2 = 5
x = (2 - 8) / 2 = -6 / 2 = -3
So, the solutions to the equation are x = 5 and x = -3.