I need help with using the quadratic formula to solve this equation:
2^x2-2x = 8
To solve the equation 2x^2 - 2x = 8 using the quadratic formula, we first need to rearrange it into the standard form of a quadratic equation: ax^2 + bx + c = 0.
In this case, our equation is already in the correct form: 2x^2 - 2x - 8 = 0.
Now, we can identify the values of a, b, and c:
a = 2
b = -2
c = -8
The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Let's substitute the values of a, b, and c into the formula:
x = (-(-2) ± √((-2)^2 - 4 * 2 * -8)) / (2 * 2)
Simplifying the equation further:
x = (2 ± √(4 + 64)) / 4
x = (2 ± √68) / 4
Now, we can simplify the square root of 68:
x = (2 ± √(4 * 17)) / 4
x = (2 ± 2√17) / 4
Lastly, we can simplify the expression by dividing both the numerator and denominator by 2:
x = (1 ± √17) / 2
Therefore, the solutions for the equation 2x^2 - 2x = 8 when using the quadratic formula are:
x = (1 + √17) / 2
x = (1 - √17) / 2