Question

Solve the quadratic equation below by completing the square. What are the solutions?

x2 + 10x + 22 = 31

Answer 1

well a perfect square is

\[(x + a)^2 = x^2 + 2ax + a^2\]

so halve the coefficient of x

then square it....

that's the value you need on the left hand side of the equation to have a perfect square.

you also need to add that value to the right hand side of the equation.

once you have it the method for the solution is

1. square root of both sides

2. subtract a from both sides


if \[(x +a)^2 = b\]

then

\[x + a = \pm \sqrt{b}\]

and

\[x = -a \pm \sqrt{b}\]

hope it all helps