Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 + 2x = 17

need the awnswer now!!

Answer 1

x = -5.24 or x = 3.24

Explanation:

`(a+b)^2=a^2+2ab+b^2\qquad(8)\\\\x^2+2x=17\\\\x^2+(2)(x)(1)=17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\\underbrace{x^2+(2)(x)(1)+1^2}_((*))=17+1^2\\\\(x+1)^2=18\iff x+1=\pm√(18)\qquad\text{subtract 1 from both sides}\\\\x=-1\pm√(18)\\\\x\approx-1-4.24=-5.24\ \vee\ x\approx-1+4.24=3.24`