Answer:
[tex]\bold{x_1=\dfrac{7+\sqrt{29}}2\ ,\qquad x_2=\dfrac{7-\sqrt{29}}2}[/tex]
Step-by-step explanation:
[tex]x^2 - 7x+9 = 4\\\\\underline{x^2 - 2\cdot x\cdot\frac72+\big(\frac72\big)^2}-\big(\frac72\big)^2+9 = 4\\\\\big(x-\frac72\big)^2-\frac{49}4+9 = 4\\\\ \big(x-\frac72\big)^2=\frac{49}4-\frac{36}4+\frac{16} 4\\\\ \big(x-\frac72\big)^2=\frac{29}4\\\\ x-\frac72=\pm\sqrt{\frac{29}4}\\\\ x=\frac72\pm\frac{\sqrt{29}}2[/tex]
