Final answer:
The values of x for which g(x) = 2x² + 9x - 56 equals zero are found using the quadratic formula. The solutions are x = 3.5 and x = -8 after applying the relevant coefficients to the formula and simplifying the equation.
Step-by-step explanation:
To find the values of x for which g(x) = 2x² + 9x - 56 equals zero, we will use the quadratic formula. The quadratic formula is x = [-b ± √(b²-4ac)] / (2a), where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0. In our case, a is 2, b is 9, and c is -56.
Applying these to the quadratic formula, we get:
x = [-(9) ± √((9) ² - 4(2)(-56))] / (2(2))
x = [-9 ± √(81 + 448)] / 4
x = [-9 ± √(529)] / 4
x = [-9 ± 23] / 4
There are two possible solutions:
x = (-9 + 23) / 4
x = 14 / 4
x = 3.5
and
x = (-9 - 23) / 4
x = -32 / 4
x = -8
Therefore, the values of x for which g(x) = 0 are 3.5 and -8.