Answer:
121/4
Step-by-step explanation:
To complete the square, we have to work with the coefficient of x
We have to divide the coefficient of x by 2, square it and add it to both sides
So we divide 11 by 2; which is 11/2; then square it
we have this as 121/4
This number is what we are going to have added
Answer:
Step-by-step explanation:
[tex]x^2+11x-38=0\\\\x^2+2\cdot\frac{11}2x-38=0\\\\\underline{x^2+2\cdot x\cdot\frac{11}2+\bold{\big(\frac{11}2\big)^2}}-\big(\frac{11}2\big)^2-38=0\qquad\qquad\qquad\{\big(\frac{11}2\big)^2=\frac{121}4\}\\\\ \big(x+\frac{11}2\big)^2-\frac{121}4-\frac{152}4=0\\\\ \big(x+\frac{11}2\big)^2-\frac{273}4=0\\\\ \big(x+\frac{11}2\big)^2=\frac{273}4[/tex]
[tex]x+\frac{11}2=\pm\frac{\sqrt{365}}2 \\\\x=\frac{-11\pm\sqrt{365}}2[/tex]
