Final answer:
To solve the equation using the quadratic formula, we identify a = 7, b = -14, and c = -56, then plug these into the formula to find two solutions, x = 4 and x = -2.
Step-by-step explanation:
To solve the quadratic equation y = 7x2 - 14x - 56 using the quadratic formula, we first need to write the equation in the standard quadratic form ax2 + bx + c = 0. For this equation, a = 7, b = -14, and c = -56. The quadratic formula is given by x = (-b ± √(b2 - 4ac)) / (2a).
Plugging the values into the quadratic formula:
x = (14 ± √((-14)2 - 4*7*(-56))) / (2*7)
x = (14 ± √(196 + 1568)) / 14
x = (14 ± √(1764)) / 14
x = (14 ± 42) / 14
Therefore, we have two solutions:
- x = (14 + 42) / 14 = 56 / 14 = 4
- x = (14 - 42) / 14 = -28 / 14 = -2
So, the solutions to the quadratic equation are x = 4 and x = -2.