Question

If using the method of completing the square to solve the quadratic equation x^2+11x-38=0 which number would have to be added to "complete the square"?

Answer 1

Answer:

           You need to add   $\dfrac{121}4$

Step-by-step explanation:

$x^2+11x-38=0\\\\x^2+2\cdot\frac{11}2x-38=0\\\\\underline{x^2+2\cdot x\cdot\frac{11}2+\bold{\big(\frac{11}2\big)^2}}-\big(\frac{11}2\big)^2-38=0\qquad\qquad\qquad\{\big(\frac{11}2\big)^2=\frac{121}4\}\\\\ \big(x+\frac{11}2\big)^2-\frac{121}4-\frac{152}4=0\\\\ \big(x+\frac{11}2\big)^2-\frac{273}4=0\\\\ \big(x+\frac{11}2\big)^2=\frac{273}4$

$x+\frac{11}2=\pm\frac{\sqrt{365}}2 \\\\x=\frac{-11\pm\sqrt{365}}2$

Answer 2

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