Question

Solve the quadratic equation by completing the square.x^2+18x+75=0First choose the appropriate form and fill in the blanks with the with the correct numbers. Then solve the equation. If there is more than one solution, separate them with commas.

Answer 1

we have the quadratic equation

x^2+18x+75=0

complete the square

x^2+18x=-75

x^2+18x+81=-75+81

x^2+18x+81=6

rewrite as perfect squares

(x+9)^2=6

Find out the solutions

square root both sides

`x+9=\pm\sqrt[\square]{6}`
`x=-9\pm\sqrt[\square]{6}`

The first solution is

`x=-9+\sqrt[\square]{6}`

The second solution is

`x=-9-\sqrt[\square]{6}`