Question

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

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

x 2 - 7x + 70 = 0
x 2 - 7x + 10 = 0
x 2 + 7x - 10 = 0

Answer 1

x 2 -7x-10=0 or x 2 -7x+10=0

Answer 2

`x^2=7x-10\\\\ x^2-7x+10=0 \ Answer \\\\ x^2-2x-5x+10=0\\\\x(x-2)-5(x-2)=0\\\\ (x-2)(x-5)=0\\\\ x-2=0\vee x-5=0 \\\\ x=2 \vee x=5`
2 Solutions



`x^2=7x-10\\\\1)\\\\ x=2\\\ 2^2=7\cdot 2-10\\\\ 4=14-10\\\\4=4\\\\ 2)\\\\x=5\\\ 5^2=7\cdot 5+10\\\\ 25=35-10\\\\ 25=25`