Final answer:
To solve the quadratic equation 5x² - 33x - 14, we use the quadratic formula and plug in the values to find the two possible solutions for x.
Step-by-step explanation:
To solve the quadratic equation 5x² - 33x - 14, we want to rearrange it into the standard form ax² + bx + c = 0. Given is already in this format with 'a' as 5, 'b' as -33, and 'c' as -14. We can then apply the quadratic formula which is x = (-b ± √(b² - 4ac)) / (2a) to find the values of x.
Plugging in the values from the equation, we get x = (33 ± √((-33) ² - 4*5*(-14))) / (2*5). Calculate the discriminant (the part under the square root) first, then solve for the two possible values of x by doing the addition and subtraction separately for each case.
Once solved, you will have the two possible values for x that satisfy the quadratic equation 5x² - 33x - 14 = 0.