If number is added to its square, the result is 56. find the number.

Given the numerical statement:

The number added to its square, the result is 56.

Find the number

Solution;:

The given numerical statement can be written as,

x^2 + x = 56

x^2 + x - 56

a =  1

b= 1

c = -56

Determine the value of the number.

In order to determine the value of  the number, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is 1, and when multiplied, the answer is -56 Hence, if we are unable to find the number, we will use the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a
x = −1 ± √(1^2 − 4(-56)(1))/2(1)
x = −1 ± √(225)/2
x = −1 ± 15/2

Solve for + - separately.

x = -1 + 15 / 2

x = 14/2

x = 7

x = -1 - 15 /2

x = -16/2

x = -8

Final answer:
The two numbers that -8 and 7.