Final answer:
To solve the quadratic equation 0=2x^2-10x+7, we apply the quadratic formula with the coefficients a=2, b=-10, and c=7 to find the two solutions x=(5+√11)/2 and x=(5-√11)/2.
Step-by-step explanation:
The solution to the quadratic equation 0 = 2x2 - 10x + 7 can be found using the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a). For this equation, the values of a, b, and c from the standard form ax2+bx+c=0 are a=2, b=-10, and c=7.
First, calculate the discriminant (the expression under the square root in the quadratic formula):
d = b2 - 4ac = (-10)2 - 4(2)(7) = 100 - 56 = 44.
Next, apply the quadratic formula:
x = (-(-10) ± √44) / (2(2)) = (10 ± √44) / 4.
Then, simplify the roots:
x = (10 ± 2√11) / 4.
Finally, simplify the fractions to get the two solutions:
x = (5 ± √11) / 2.
Thus, the solution to the quadratic equation 2x2 - 10x + 7 is x = (5 + √11) / 2 and x = (5 - √11) / 2.