Answer:
x=9, x=2
Explanation:
Since both expressions (x^2 - 14x + 23 and -3x+5) are equal to y, set those expressions equal to each other and solve for x.
x^2 - 14x + 23 = -3x + 5
subtract 5 from both sides
x^2 - 14x + 23 - 5 = -3x + 5 - 5
x^2 - 14x + 18 = -3x
add 3x to both sides
x^2 - 14x + 3x + 18 = -3x + 3x
x^2 - 11x + 18 = 0x
factor.
(x-9)(x-2) = 0
Because the product of these two things equals 0, we know that one of these terms must equal to zero.
x-9 = 0 or x-2 = 0
it can be either, so solve for both.
x-9 + 9 = 0 + 9 or x-2 + 2 = 0 + 2
x = 9 or x=2