Final answer:
The solutions to the quadratic equation x^2 + 14x + 40 = 0 are found by substituting into the quadratic formula. The solutions are x = -4 and x = -10. Correct option is c)
Step-by-step explanation:
The solutions to the quadratic equation x^2 + 14x + 40 = 0 can be found using the quadratic formula, which is expressed as x = [-b ± √(b^2 - 4ac)] / (2a). In this equation, a, b, and c are coefficients corresponding to the terms of the quadratic equation respectively.
To solve for x, we substitute a = 1, b = 14, and c = 40 into the formula, which gives us:
x = [-14 ± √(14^2 - 4*1*40)] / (2*1)
x = [-14 ± √(196 - 160)] / 2
x = [-14 ± √36] / 2
x = [-14 ± 6] / 2
Thus, we have two solutions:
- x = (-14 + 6) / 2 which simplifies to x = -4
- x = (-14 - 6) / 2 which simplifies to x = -10
Therefore, the solutions to the equation are x = -4 and x = -10, which correspond to answer choice (c).