Question

Solve the equation by using the Quadratic Formula. Round to the nearest tenth, if necessary. Write your solutions from least to greatest.

separated by a comma, if necessary. If there are no real solutions, write no solutions.
x² + 4x = -1

Answer 1

x = -2 - sqrt(3), -2 + sqrt(3)

Explanation:

We can rewrite the equation as

x² + 4x + 1 = 0

Now we can use the quadratic equation.

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = 4, c = 1. Substituting these values ​​gives:

x = (-4 ± sqrt(4² - 4(1)(1))) / 2(1)

x = (-4 ± sqrt(16 - 4)) / 2

x = (-4 ± sqrt(12)) / 2

x = (-4 ± 2sqrt(3)) / 2

x = -2 ± sqrt(3)

So, from min to max, the solution is:

x = -2 - sqrt(3), -2 + sqrt(3)

Hope this helps!