The square of a number is equal to the sum of 21 and 4 times the number. Find the number
let the number be x
translate into math
x^2 = 21 + 4x
x^2 - 4x - 21 = 0
(x-7)(x+3) = 0
x = 7 or x = -3
the number is either 7 or -3
check:
if the number is 7
the square of the number is 49
21 plus 4(7) = 49 , yeahh!
if the number is -3
the square of the number is 9
21 + 4(-3) = 9, yeahhh!
Both numbers work.
To find the number, let's start by translating the problem into an equation.
Let's assume the number is represented by "x." According to the problem statement, the square of the number is equal to the sum of 21 and four times the number.
So, the equation can be written as:
x^2 = 21 + 4x
To solve this equation, we need to rearrange it into a quadratic equation form:
x^2 - 4x - 21 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case.
To factor the equation, we need to find two numbers whose product is -21 and whose sum is -4 (the coefficient of the middle term).
After some trial and error, we find that -7 and 3 satisfy these conditions. So, we can rewrite the equation as:
(x - 7)(x + 3) = 0
Setting each factor equal to zero gives us two possible solutions:
x - 7 = 0 or x + 3 = 0
Solving these equations, we find:
x = 7 or x = -3
Therefore, the two possible values for the number are 7 and -3.