Question

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation? {–7, 1} (negative 3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot) (3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot) {1, 7}

Answer 1

The two solutions are x = -7 and x = 1

Explanation:

We complete the square for the expression on the left of the equal sign, by adding the "square of half of the coefficient of the term in x". That is, in our case we need to add
`((6)/(2))^2=(3)^2=9`

So we proceed to add 9 on both sides of the equation, that way completing a perfect square trinomial on the left side of the equal sign:

`x^2+6x=7\\x^2+6x+9=7+9\\x^2+6x+9=16`

Notice now that the perfect square on the left is
`(x+3)^2`, so we replace it in our equation:

`x^2+6x+9=16\\(x+3)^2=16\\x+3=+/-√(16) \\x+3=+/-4`

Therefore, we get two possible solutions:

a)
`x+3=4\\x=4-3\\x=1`, and

b)
`x+3=-4\\x=-4-3\\x=-7`

So our two solutions are x= -7 and x=1