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Anestetic [448]
3 years ago
12

Solve the equation by completing the square.Round to the nearest hundredth if necessary. X^2–x–7=0

Mathematics
1 answer:
lesya [120]3 years ago
5 0
NOTE:  \left(x-\dfrac{1}{2}\right)^2=x^2-x+\dfrac{1}{4}

x^2-x-7=0 \\ \\ \underbrace{x^2-x+\frac{1}{4}}_{\left(x-\frac{1}{2}\right)^2}-7\dfrac{1}{4}=0 \\ \\  \\ \left(x-\frac{1}{2}\right)^2=7\frac{1}{4}=\frac{29}{4} \qquad /\sqrt{}\\ \\  \left|x-\frac{1}{2}\right|=\dfrac{\sqrt{29}}{2} \\ \\  x_1=\dfrac{1}{2}-\dfrac{\sqrt{29}}{2} \approx  -2.19 \\ \\ x_2=\dfrac{1}{2}+\dfrac{\sqrt{29}}{2} \approx 3.19

ANSWER:  c)

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