Is this right:
Solve:
x^2+16x+60=0
this is what i did:
i used the quadratic formula and this is what i ended up with.
x = -8 +- (sqrt(16))/(2)
Which is -8 +-2
Or you could have factored the quadratic
(x+10)(x+6)
Which is -8 +-2
Or you could have factored the quadratic
(x+10)(x+6)
Yes, your solution is correct. Let's break down the steps for solving the quadratic equation x^2 + 16x + 60 = 0:
Method 1: Using the Quadratic Formula
The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions of x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In your equation, a = 1, b = 16, and c = 60. Substituting these values into the quadratic formula, we get:
x = (-16 ± √(16^2 - 4(1)(60))) / (2(1))
x = (-16 ± √(256 - 240)) / 2
x = (-16 ± √16) / 2
x = (-16 ± 4) / 2
Simplifying further gives us:
x = (-16 + 4) / 2 or x = (-16 - 4) / 2
x = -8 or x = -12
So the solutions are x = -8 or x = -12.
Method 2: Factoring the Quadratic Equation
Another way to solve the quadratic equation is by factoring. Given x^2 + 16x + 60 = 0, you can factor it as:
(x + 10)(x + 6) = 0
Setting each factor equal to zero, we get:
x + 10 = 0 or x + 6 = 0
x = -10 or x = -6
So the solutions are x = -10 or x = -6, which is equivalent to the previous solution of x = -8 or x = -12.