Question

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

a. 2.6, 2.69
b. –6.75,7.75
c. 3.19, –2.19
d. 3.05, –2.05

Answer 1

NOTE:
`\left(x-(1)/(2)\right)^2=x^2-x+(1)/(4)`


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

ANSWER: c)