Final answer:
To solve the quadratic equation 2v²+6v-6=0, we can use the quadratic formula. The solutions are approximately v ≈ 0.732 and v ≈ -3.732.
Step-by-step explanation:
To solve the quadratic equation 2v²+6v-6=0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax²+bx+c=0, the solutions for x are given by:
x = (-b ± √(b²-4ac))/(2a)
In our equation, a=2, b=6, and c=-6. Plugging these values into the quadratic formula, we get:
x = (-6 ± √(6²-4(2)(-6)))/(2(2))
Simplifying further, we have:
x = (-6 ± √(36+48))/(4)
x = (-6 ± √(84))/(4)
Now, let's find the two possible solutions for x by calculating the square root of 84 and solving for x using both the positive and negative square root:
x ≈ (-6 + √84)/(4) ≈ 0.732
x ≈ (-6 - √84)/(4) ≈ -3.732
Therefore, the solutions to the quadratic equation 2v²+6v-6=0 are approximately v ≈ 0.732 and v ≈ -3.732.