what is a number where the square of itself is 195 more than twice the number
What two whole numbers is the following square root between?
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a
12-13
b
13-14
c
14-15
d
15-16
To find the number where the square of itself is 195 more than twice the number, we'll need to set up an equation and solve for the unknown number.
Let's assume the unknown number is "x".
According to the given information, the square of the number is 195 more than twice the number. Mathematically, this can be represented as:
x^2 = 2x + 195
We need to solve this quadratic equation to find the value of x.
To solve this equation, we first rearrange it to bring all terms to one side:
x^2 - 2x - 195 = 0
Now, we can solve this quadratic equation by either factoring, completing the square, or using the quadratic formula.
After simplifying the equation, it factors to:
(x - 15)(x + 13) = 0
Setting each factor equal to zero, we have two solutions:
x - 15 = 0 => x = 15
x + 13 = 0 => x = -13
Therefore, the two possible numbers where the square of itself is 195 more than twice the number are 15 and -13.
x^2 = 195 +2 x
x^2 - 2 x - 195 = 0
195/15 = 13 good
(x-15)(x+13) = 0
x = 15
check
225 = 195 + 30?
yes