Solve by using the quadratic formula.
x^2 + 6x + 6 = 0
I am having problems using the quadratic formula to get the right answer. Can someone show me the steps that I use? Thanks.
Quadratic formula -b(plus or minus)squareroot(b^2-4ac) all over 2a
so you'd plug in -6(plus or minus)squareroot((6^2)-(4(1)(6)) and divide the -6 plus /\ that by 2. and then do -6 minus /\ that by 2. and you get your two solutions
-3 + or - 2sqrt 3
Sure! I can help you with that. The general form of a quadratic equation is:
ax^2 + bx + c = 0
In this case, with x^2 + 6x + 6 = 0, we can identify:
a = 1 (coefficient of x^2)
b = 6 (coefficient of x)
c = 6
To solve the quadratic equation using the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / (2a)
We substitute the values of a, b, and c into the formula and then simplify.
x = (-(6) ± √((6)^2 - 4(1)(6))) / (2(1))
x = (-6 ± √(36 - 24)) / 2
x = (-6 ± √12) / 2
Now, we simplify the two possible solutions:
x = (-6 + √12) / 2
x = (-6 + 2√3) / 2
x = -3 + √3
x = (-6 - √12) / 2
x = (-6 - 2√3) / 2
x = -3 - √3
So, the solutions to the quadratic equation x^2 + 6x + 6 = 0 are:
x = -3 + √3
x = -3 - √3
And those are the steps to solve a quadratic equation using the quadratic formula. I hope this helps!