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Taya2010 [7]
2 years ago
6

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

Mathematics
1 answer:
earnstyle [38]2 years ago
4 0

Answer:

<h2>x = -5.24 or x = 3.24</h2>

Step-by-step 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\sqrt{18}\qquad\text{subtract 1 from both sides}\\\\x=-1\pm\sqrt{18}\\\\x\approx-1-4.24=-5.24\ \vee\ x\approx-1+4.24=3.24

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