when the square of a number is increased by 10, the result is seven times the original number. find the number
x ^ 2 + 10 = 7 x Subtract 7 x to both sides
x ^ 2 + 10 - 7 x = 7 x - 7 x
x ^ 2 - 7 x + 10 = 0
Now you must solve this quadratic equation.
The solutions are :
x = 2 and x = 5
Proof :
2 ^ 2 + 10 = 4 + 10 = 14 = 7 * 2
5 ^ 2 + 10 = 25 + 10 = 35 = 7 * 5
To find the number, we can set up an equation using the given information.
Let's assume the number is represented by "x".
According to the question, when the square of the number is increased by 10, the result is seven times the original number.
This can be written as:
x^2 + 10 = 7x
To solve this equation, we need to rearrange it into a quadratic equation where one side is equal to zero:
x^2 - 7x + 10 = 0
Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -7, and c = 10.
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Let's factor the quadratic equation:
(x - 5)(x - 2) = 0
Using the zero product property, we set each factor equal to zero:
x - 5 = 0 OR x - 2 = 0
Solving for x in each equation:
x = 5 OR x = 2
Therefore, the two possible numbers are x = 5 and x = 2.