Solve the problem.
-The sum of a number and its square is 56. Find the number.
A) 7 or 8
B) -7 or 8
C) 7 or -8
D) -7 or -8

Question

Quizplus · Accepted Answer

Let the number be x. According to the problem, x + x^2 = 56. Rewriting this equation as x^2 + x - 56 = 0, we can solve for x using the quadratic formula. This gives us x = 7 or x = -8. Therefore, the answer is C) 7 or -8. Let's call the number we are trying to find "x".

From the problem, we know that:

x + x^2 = 56

We can rearrange it to get:

x^2 + x - 56 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± sqrt(b^2 - 4ac))/2a

Where:

a = 1 
b = 1 
c = -56

Plugging in those values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-56)))/2(1)

Simplifying:

x = (-1 ± sqrt(1 + 224))/2

x = (-1 ± sqrt(225))/2

x = (-1 ± 15)/2

The two possible solutions are:

x = (-1 + 15)/2 = 7 
x = (-1 - 15)/2 = -8

Therefore, the answer is choice C.

Solve the Problem. -The Sum of a Number and Its Square Is 56