Question

Solve the equation using the quadratic formula. x² +11x+28=0. The solution set is?

a) x=−4,−7
b) x=4,7
c) x=−5,−6
d) x=5,6

Answer 1

The solution set to the quadratic equation x² + 11x + 28 = 0 using the quadratic formula is x = -4, -7, corresponding to option (a).

Step-by-step explanation:

The correct answer is option (a), which states that the solution set is x=-4, -7. To solve the quadratic equation x² + 11x + 28 = 0 using the quadratic formula, we identify the coefficients a=1, b=11, and c=28. The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

To solve the quadratic equation x² + 11x + 28 = 0 using the quadratic formula, we need to identify the values of a, b, and c. In this equation, a = 1, b = 11, and c = 28.

Substituting these values into the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we get:

x = (-11 ± √(11² - 4(1)(28))) / (2(1))

Simplifying further, we have:

x = (-11 ± √(121 - 112)) / 2

x = (-11 ± √9) / 2

x = (-11 ± 3) / 2

Substituting the coefficients into the formula gives us x = (-11 ± √((11²) - 4(1)(28))) / (2(1)). Calculating the values under the square root, 11² - 4(1)(28) equals 121 - 112, which simplifies to 9. Our formula now becomes x = (-11 ± √9) / 2. The square root of 9 is 3, so we have two possible solutions: x = (-11 + 3) / 2 and x = (-11 - 3) / 2. The solutions are x = -4 and x = -7.