What are the exact solutions of x2 equals 5x plus 2?

Answer 1

x^(2) = 5x + 2

x^(2) - 5x - 2 = 0

This does NOT factor so apply the Quadratic Eq;n

x = { - - 5 +/- sqrt[(-5)^2 - 4(1)(-2) }} / 2(1)

x = { 5 +/- sqrt[25 + 8]} / 2

x = { 5 +/- sqrt(33)} / 2

x= { 5 +/- 5.7445... } / 2

x = 10.7445... / 2 = 5.37228....

&

x = -0.7445626... / 2 = -0.37228...

Answer 2

The exact solutions are [5 ± sqrt(33)]/2.

The approx values are -0.3723 and 5.3723