How can i solve for this would it best to factor or use the quadratic formula.

solve: x^2+2x-8=0

How about for this problem as well:

solve : x^2+7x-1 = 0

in the first, can you think of two multipliers of -8 that have a sum of 2??
how about 4 and -2
so it factors!

in the second, are there any factors of -1 that have a sum of 7????
not very likely, so use the formula

To solve the equation x^2+2x-8=0, you can use factoring or the quadratic formula. Let's explore both methods:

1. Factoring:
To factor the equation x^2+2x-8=0, we need to find two numbers that multiply to -8 and add up to 2. After trying different pairs of numbers, we find that 4 and -2 satisfy these conditions. So, we can rewrite the equation as (x+4)(x-2) = 0. By setting each factor equal to zero, we get two solutions: x+4=0 (which leads to x=-4) and x-2=0 (which leads to x=2). Therefore, the equation is solved, and the solutions are x=-4 and x=2.

2. Quadratic Formula:
Another way to solve the equation x^2+2x-8=0 is to use the quadratic formula, which states that for any quadratic equation of the form ax^2+bx+c=0, the solutions can be found using the formula:

x = (-b ± √(b^2-4ac))/(2a)

For the equation x^2+2x-8=0, we have a=1, b=2, and c=-8. Substituting these values into the quadratic formula, we get:

x = (-2 ± √(2^2-4(1)(-8)))/(2(1))

Simplifying further,

x = (-2 ± √(4+32))/2

x = (-2 ± √36)/2

x = (-2 ± 6)/2

Now, we have two possibilities:

- When taking the positive root:

x = (-2 + 6)/2

x = 4/2

x = 2

- When taking the negative root:

x = (-2 - 6)/2

x = -8/2

x = -4

So, using the quadratic formula, we also find that the solutions to the equation are x=-4 and x=2.

In summary, both factoring and using the quadratic formula will lead you to the correct solutions for the equation x^2+2x-8=0. You can choose the method that you find more convenient or easier to apply.