Question

Solve perfect square equation
х^2 +6х + 9 = 8​

Answer 1

`\large\boxed{x=-3-2\sqrt2\ \vee\ x=-2+2\sqrt2}`

Explanation:

`x^2+6x+9=8\\\\x^2+2(x)(3)+3^2=8\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+3)^2=8\iff x+3=\pm\sqrt8\\\\x+3=\pm√(4\cdot2)\\\\x+3=\pm\sqrt4\cdot\sqrt2\\\\x+3=\pm2\sqrt2\qquad\text{subtract 3 from both sides}\\\\x=-3-2\sqrt2\ \vee\ x=-2+2\sqrt2`