What is a solution of x2 + 6x = -5?
first, rearrange things in the standard form:
x^2 + 6x + 5 = 0
Now, which two factors of 5 add up to 6?
well, 5 is prime, so the only factors are 1,5
(x+1)(x+5) = 0
why do we always set up the list of factors = 0?
because if the product of two number is zero, one or the other of them must be zero! That means we must have either
x+1 = 0
or
x+5 = 0
So, the solutions are x = -1, -5
To find the solution of the quadratic equation x^2 + 6x = -5, we need to solve it for x. Here are the steps:
Step 1: Rewrite the equation in standard form.
x^2 + 6x + 5 = 0
Step 2: Factor the quadratic equation.
(x + 5)(x + 1) = 0
Step 3: Set each factor equal to zero and solve for x.
x + 5 = 0 or x + 1 = 0
For x + 5 = 0:
x = -5
For x + 1 = 0:
x = -1
So, the solutions of the equation x^2 + 6x = -5 are x = -5 and x = -1.
To find the solution to the equation x^2 + 6x = -5, we need to solve for x. The equation is in the form of a quadratic equation, which can be solved through factoring, completing the square, or using the quadratic formula.
In this case, let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = 6, and c = -5.
Plugging these values into the quadratic formula, we get:
x = (-6 ± sqrt(6^2 - 4(1)(-5))) / (2(1))
Simplifying further:
x = (-6 ± sqrt(36 + 20)) / 2
x = (-6 ± sqrt(56)) / 2
x = (-6 ± sqrt(4 * 14)) / 2
x = (-6 ± 2sqrt(14)) / 2
Now, we can simplify the expression:
x = -3 ± sqrt(14)
Therefore, the solutions to the equation x^2 + 6x = -5 are:
x = -3 + sqrt(14)
x = -3 - sqrt(14)