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Olin [163]
3 years ago
14

Use completing the square to solve (x-12)(x+4)=9 for x

Mathematics
2 answers:
Kay [80]3 years ago
6 0
X= 4 + \sqrt{73}

x= 4 - \sqrt{73}
cestrela7 [59]3 years ago
6 0

we have

(x-12)(x+4)=9\\ x^{2} +4x-12x-48=9\\ x^{2} -8x-48=9

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2} -8x=9+48\\ x^{2} -8x=57

Complete the square. Remember to balance the equation by adding the same constants to each side

x^{2} -8x+16=57+16\\ x^{2} -8x+16=73

Rewrite as perfect squares

x^{2} -8x+16=73\\ (x-4)^{2} =73\\ (x-4)=(+/-)\sqrt{73}

x1=4+\sqrt{73} \\ x2=4-\sqrt{73}

therefore

the answer is

x1=4+\sqrt{73} \\ x2=4-\sqrt{73}



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