SOLUTION: x^2+6x=7 Solve by completing the square to obtain exact solutions.

Question 77506: x^2+6x=7
Solve by completing the square to obtain exact solutions.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Subtract 7 from both sides

Set the expression equal to y

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

Start with the given equation

Add to both sides

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Distribute

Multiply

Now add to both sides to isolate y

Combine like terms

Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.

Check:

Notice if we graph the original equation we get:

Graph of . Notice how the vertex is (,).

Notice if we graph the final equation we get:

Graph of . Notice how the vertex is also (,).

So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.

So our equation can be converted into vertex form:

Let y=0

Add 16 to both sides

Take the square root of both sides

Which means:

or

or Subtract 3 from both sides for each case

So our solutions are:

or
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