Question

The square of a number is equal to 10 less than 7 thnes that number. What are the two possible solutions?

Which of the following equations is used in the process of solving this problem?

Answer 1

2, 5

Explanation:

Let the number be x.

`\therefore \: {x}^(2) = 7x - 10 \\ \therefore \: {x}^(2) - 7x + 10 = 0 \\ \therefore \: {x}^(2) - 5x - 2x + 10 = 0 \\ \therefore \:x( {x} - 5) - 2(x - 5) = 0 \\ \therefore \:(x - 5)(x - 2) = 0 \\ \therefore \:x - 5 = 0 \: \: or \: \: x - 2 = 0 \\ \therefore \:x = 5 \: \: or \: \: x = 2 \\ \huge \red{ \boxed{\therefore \:x = \{2, \: \: 5 \}}}`

Hence, the two possible solutions are 2 and 5.