SOLUTION: Solve by completing the square: x^2+4x-5=0

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Question 178395This question is from textbook
: Solve by completing the square: x^2+4x-5=0 This question is from textbook

Answer by jim_thompson5910(33401) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B4x-5 Start with the given expression.

Take half of the x coefficient 4 to get 2. In other words, %281%2F2%29%284%29=2.

Now square 2 to get 4. In other words, %282%29%5E2=%282%29%282%29=4

x%5E2%2B4x%2Bhighlight%284-4%29-5 Now add and subtract 4. Make sure to place this after the "x" term. Notice how 4-4=0. So the expression is not changed.

%28x%5E2%2B4x%2B4%29-4-5 Group the first three terms.

%28x%2B2%29%5E2-4-5 Factor x%5E2%2B4x%2B4 to get %28x%2B2%29%5E2.

%28x%2B2%29%5E2-9 Combine like terms.

So after completing the square, x%5E2%2B4x-5 transforms to %28x%2B2%29%5E2-9. So x%5E2%2B4x-5=%28x%2B2%29%5E2-9.

So x%5E2%2B4x-5=0 is equivalent to %28x%2B2%29%5E2-9=0.


Now let's solve %28x%2B2%29%5E2-9=0

%28x%2B2%29%5E2-9=0 Start with the given equation.

%28x%2B2%29%5E2=0%2B9Add 9 to both sides.

%28x%2B2%29%5E2=9 Combine like terms.

x%2B2=0%2B-sqrt%289%29 Take the square root of both sides.

x%2B2=sqrt%289%29 or x%2B2=-sqrt%289%29 Break up the "plus/minus" to form two equations.

x%2B2=3 or x%2B2=-3 Take the square root of 9 to get 3.

x=-2%2B3 or x=-2-3 Subtract 2 from both sides.

x=1 or x=-5 Combine like terms.



So the solutions are x=1 or x=-5.