What is the solution set for the quadratic equation x^2 + 6x = -5? I’m honestly confused and don’t know what to do. I don’t think the answer could be F {1} or J {-5} because it says sets. Which leaves me with G {-1,-5} and H{1,5}. Help?
x^2 + 6x = -5
x^2 + 6x + 5 = 0
(x+1)(x+5) = 0
x=-1,x=-5
written as a set, {-1,-5}
What part confuses you?
To find the solution set for the quadratic equation x^2 + 6x = -5, we can start by rearranging the equation to bring all terms to one side:
x^2 + 6x + 5 = 0
Now, we need to solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula, which states that for a quadratic equation ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation x^2 + 6x + 5 = 0, we have a = 1, b = 6, and c = 5. Substituting these values into the formula, we get:
x = (-6 ± √(6^2 - 4*1*5)) / (2*1)
Simplifying further:
x = (-6 ± √(36 - 20)) / 2
x = (-6 ± √16) / 2
x = (-6 ± 4) / 2
Now let's find the two possible solutions:
For x = (-6 + 4) / 2, we have x = -2 / 2, which reduces to x = -1.
For x = (-6 - 4) / 2, we have x = -10 / 2, which reduces to x = -5.
Therefore, the solution set for the quadratic equation x^2 + 6x = -5 is {x = -1, x = -5}, which is option G.
To find the solution set for the quadratic equation x^2 + 6x = -5, we need to solve for x. Here's how you can do it step by step:
Step 1: Rewrite the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, we have:
x^2 + 6x + 5 = 0
Step 2: Determine the values of a, b, and c. In our equation, a = 1, b = 6, and c = 5.
Step 3: Apply the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, the formula becomes:
x = (-6 ± √(6^2 - 4(1)(5))) / (2(1))
x = (-6 ± √(36 - 20)) / 2
x = (-6 ± √16) / 2
x = (-6 ± 4) / 2
Step 4: Simplify the expression:
x1 = (-6 + 4) / 2 = -2 / 2 = -1
x2 = (-6 - 4) / 2 = -10 / 2 = -5
So, the solution set for the quadratic equation x^2 + 6x = -5 is {-1, -5}. Thus, the correct option is G {-1, -5}.