The square of a negative number is eight more than twice the negative number. Find the number.

Question

I do not know where to start.

Answer 1

Let the number = -x

 

 

(-x)² = 2(-x) + 8

 

 

Solve for x.

 

x² = -2x + 8

 

 

Add 2x and subtract 8 on both sides of equation.

 

x² + 2x - 8 = 0

 

 

Factor using FOIL.

 

(x + 4)(x - 2) = 0

 

 

Set the factors equal to zero and solve for x.

 

x + 4 = 0            and             x - 2 = 0

 

x = -4                 and             x = 2

 

 

Since our defined variable already has a negative sign in front of x, we take the positive value of x.

 

x = 2

 

 

So the number is -2.

 

 

Answer 2

Hello, thank you for taking the time to post your question!

The key on this type of question is to set up an algebraic expression based on the information given. On this one we have

x^2 = 8 + 2x    with the added caveat that the number is negative

From there then I would solve for the value of x algebraically, meaning

x^2 – 2x – 8 = 0

(x – 4)(x + 2) = 0

x = 4   OR   x = -2

between those two possible solutions then the value that we want to pick is x = -2 because it’s saying that the number must be negative

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 3

From the information given we can set up an equation.

 

x² = 2x + 8    where  x<0

 

Moving everything to the left side we have a quadratic equation:

 

x²-2x-8 = 0

 

The quadratic equation says  x = [-b ±√(b²-4ac)]/2a

In this case a = 1, b = -2, c = -8

 

x = [2 ±√((-2)²-4(1)(-8)) ]/(2)(1)

  = [2 ±√(4 + 32)]/2

  = (2 ±√36)/2

  = (2 ± 6)/2

 = 4 or -2

 

Since x is a negative number our answer is x = -2

 

Check:  x² = 2x + 8

          (-2)² = 2(-2) + 8

            4 = -4 + 8

            4 = 4

Our answer fits the conditions given

 

Note:  We could actually have factored our quadratic equation

x²-2x-8 = 0

The factors of -8 that add to -2 are  (-4)(2) so this factors to

(x-4)(x+2) = 0

 

x = 4 or x = -2

 

Again, we take the negative answer so x = -2