Respuesta :
The solution is x = 1 and x = -3
Solution:
Given that we have to solve the given equation by factoring
Given equation is:
[tex]x^2=2x + 3\\\\x^2 - 2x - 3 = 0[/tex]
[tex]\text{Consider the form } x^2+bx+c[/tex]
Find a pair of integers whose product is c and and whose sum is b
[tex]\text{Compare } x^2-2x-3 = 0 \text{ with } x^2+bx +c\\\\\text{We get } b = -2 \text{ and } c = -3[/tex]
Now find, a pair of integers whose sum is -2 and product is -3
The integers that satisfies this condition is -1 and 3
When we add - 1 and 3 we get 2
When multiply -1 and 3 we get -3
Thus the pair of integers are -1 and 3
Write the factored form using these integers.
[tex](x-1)(x+3) = 0[/tex]
The Zero Product Property states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0
Set the factors equal to 0
[tex]x - 1 = 0 \text{ and } x + 3 = 0[/tex]
x = 1 and x = -3
Thus the solution is x = 1 and x = -3
