Question

Solve for x in the equation 2x 2−7x+5=0.

a) x=1,5
b) x=−1,−5
c) x=2,−2
d) x=−2,1

Answer 1

To solve the equation 2x^2 - 7x + 5 = 0, we can use the quadratic formula. The two solutions for x are 2.5 and 1.

Step-by-step explanation:

To solve the equation 2x^2 - 7x + 5 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values from the equation, we get:

x = (-(-7) ± √((-7)^2 - 4(2)(5))) / (2(2))

Simplifying further:

x = (7 ± √(49 - 40)) / 4
x = (7 ± √9) / 4
x = (7 ± 3) / 4

So the two possible solutions for x are:

x = (7 + 3) / 4 = 10 / 4 = 2.5
x = (7 - 3) / 4 = 4 / 4 = 1