Final answer:
To solve the quadratic equation 2x^2 - 7x - 5 = 0, we can use the quadratic formula. The two solutions to the given equation, rounded to two decimal places, are x ≈ 1.03 and x ≈ -0.53.
Step-by-step explanation:
To find the value of x that satisfies the equation 2x^2 - 7x - 5 = 0, we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Where a, b, and c are coefficients from the quadratic equation ax^2 + bx + c = 0. For our equation, a = 2, b = -7, and c = -5.
By substituting these values into the quadratic formula, we get:
x = (-(-7) ± √((-7)^2 - 4 × 2 × (-5))) / (2 × 2)
x = (7 ± √(49 + 40)) / 4
x = (7 ± √89) / 4
We then calculate the two possible values for x to two decimal places:
x = (7 + √89) / 4 ≈ 4.11 / 4 ≈ 1.03
x = (7 - √89) / 4 ≈ -2.11 / 4 ≈ -0.53
Therefore, the two values of x that satisfy the equation 2x^2 - 7x - 5 = 0 are approximately 1.03 and -0.53, to two decimal places.