Question

Solve the equation x�� + 6x + 7 = 0.

1) -1 and -5
2) 3 plus or minus square root of 2
3) -3 plus or minus square root of 2
4) -3 plus or minus square root of 2, all over 2

Answer 1

The solutions to the equation x² + 6x + 7 = 0 are -3 ± √2.

Step-by-step explanation:

To solve the equation x² + 6x + 7 = 0, we can use the quadratic formula. For an equation of the form ax² + bx + c = 0, the roots can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

By substituting the values from the given equation, we get:

x = (-6 ± √(6² - 4(1)(7))) / (2(1))

Simplifying further, we have x = (-6 ± √(36 - 28)) / 2 = (-6 ± √8) / 2 = -3 ± √2.

Therefore, the solutions to the equation are -3 ± √2.