the square of a number is equal to the sum of 21 and 4 times the number. find the number
X=-3
X=7
RIGHT?
RIGHT!
To find the number that satisfies the given equation, let's go step by step:
1. Let's assume the number we are looking for is represented by the variable "x".
2. The square of the number is x^2.
3. The sum of 21 and 4 times the number is (21 + 4x).
4. According to the given equation, the square of the number is equal to the sum of 21 and 4 times the number:
x^2 = 21 + 4x
Now, we can solve this equation to find the possible values of "x".
To solve the quadratic equation, we can rearrange it into standard form:
x^2 - 4x - 21 = 0
Now, we can either factor the quadratic equation or use the quadratic formula to find the solutions.
Using the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation x^2 - 4x - 21 = 0,
a = 1, b = -4, c = -21
Plugging these values into the quadratic formula:
x = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1))
x = (4 ± √(16 + 84)) / 2
x = (4 ± √100) / 2
x = (4 ± 10) / 2
Now, we have two possible solutions:
1. x = (4 + 10) / 2 = 14 / 2 = 7
2. x = (4 - 10) / 2 = -6 / 2 = -3
Therefore, based on the equation x^2 = 21 + 4x, the possible values for x are -3 and 7. So, you are correct!