Question

Solve the equation by completing the square

x² – 5x +5=0​

Answer 1

Answer:

$x = \frac{5}{2} + \frac{ \sqrt{5} }{2}$

Step-by-step explanation:

${x}^{2} - 5x + 5 = 0$

${x}^{2} - 5x = - 5$

${x}^{2} - \frac{5}{1} x = - \frac{5}{1}$

${x}^{2} - 5x + ( \frac{5}{2} {)}^{2} = - 5 + ( \frac{5}{2} {)}^{2}$

$(x - \frac{5}{2} {)}^{2} = - 5 + \frac{25}{4} = \frac{5}{4}$

$x - \frac{5}{2} = + \frac{ \sqrt{5} }{4} = + \frac{ \sqrt{5} }{2}$

$x = \frac{5}{2} + \frac{ \sqrt{5} }{2}$