3k² = 8k+8
hey, you try this one the same way I did the one above.
or just use the quadratic formula
To solve the equation 3k² = 8k + 8, we need to isolate the variable k on one side of the equation. Here's how we can do it step by step:
1. Start by moving all terms to one side of the equation:
3k² - 8k - 8 = 0
2. Next, we need to factor the quadratic equation. However, it appears that this equation cannot be easily factored. So, we can solve it using the quadratic formula:
The quadratic formula states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
In our equation, a = 3, b = -8, and c = -8.
3. Substitute the values of a, b, and c into the quadratic formula to find the solutions for k:
k = (-(-8) ± √((-8)² - 4 * 3 * (-8))) / (2 * 3)
Simplifying this expression further gives:
k = (8 ± √(64 + 96)) / 6
k = (8 ± √(160)) / 6
k = (8 ± 4√10) / 6
4. Finally, we can simplify the expression by dividing both the numerator and denominator by 2:
k = (4 ± 2√10) / 3
Therefore, the solutions for the equation 3k² = 8k + 8 are k = (4 + 2√10) / 3 and k = (4 - 2√10) / 3.