Question

Which are the solutions of the quadratic equation?
x² = 7x + 4

Answer 1

`x = (7 + √(65))/(2) \ , \ x = (7 - √(65))/(2)`

Explanation:

`x^2 = 7x + 4 \\\\x^2 - 7x - 4 = 0\\\\ a = 1 \ , \ b = - 7 , \ c \ = \ - 4 \\\\x = \frac{-b \pm \sqt{b^2 - 4ac }}{2a}\\\\Substitute \ the \ values : \\\\x = (7 \pm √(7^2 - (4 * 1 * -4)))/(2 * 1)\\\\x = (7 \pm √(49 + 16))/(2 )\\\\x = (7 \pm √(65))/(2 )\\\\x = (7 + √(65))/(2)\ , \ x = (7 - √(65))/(2)`

Answer 2

X= 7/2 + 1/2 square root (65)