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?

Respuesta :

Answer:

2, 5

Step-by-step explanation:

Let the number be x.

[tex] \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 \}}}[/tex]

Hence, the two possible solutions are 2 and 5.