The sum of a negative number and its square is 56. What is the number?
x^2 + x = 56
x^2 + x - 56 = 0
(x+8)(x-7) = 0
x = -8 or 7
Looks like -8 is the answer
64 + (-8) = 6
x^2 + x = 56
x^2 + x - 56 = 0
(x+8)(x-7) = 0
x = -8 or 7
Looks like -8 is the answer
64 + (-8) = 56
To solve this problem, we can set up an equation based on the information given. Let's call the unknown number "x".
According to the problem, the sum of the number and its square is 56. So we can write the equation as:
x + x^2 = 56
Now, to find the value of "x", we can rearrange the equation to solve for "x":
x^2 + x - 56 = 0
This is a quadratic equation. We can solve it by factoring or by using the quadratic formula.
To factor, we need to find two numbers that multiply to form the constant term (-56) and add up to the coefficient of the linear term (1). In this case, the numbers are -7 and 8 since (-7) * (8) = -56 and (-7) + (8) = 1.
So, we can factor the quadratic equation as:
(x - 7)(x + 8) = 0
This means that either (x - 7) = 0 or (x + 8) = 0. Solving these two equations, we get:
x - 7 = 0 --> x = 7
x + 8 = 0 --> x = -8
So, the possible values for the number "x" are 7 and -8. However, since the problem mentioned that the number is negative, the answer is -8.