SOLUTION: Solve and show steps by completing the square: x^2+8x+13=0

Question 184184: Solve and show steps by completing the square:
x^2+8x+13=0
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract . Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

So after completing the square, transforms to . So .

So is equivalent to .

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Now let's solve

Start with the given equation.

Add to both sides.

Combine like terms.

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Simplify the square root.

or Subtract from both sides.

=====================================================

Answer:

So the solutions are or .

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Move the constant term to the right side:

Divide the coefficient on the x term by 2 and square the result. Add this result to both sides. 8 divided by 2 is 4 squared is 16:

You now have a perfect square on the left, factor it:

Take the square root of both sides, remembering to consider both the positive and negative root:

Solve for x:

John

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