SOLUTION: Hello. Use completing the square to solve each equation: x^2 - 4x + 30 = 0 thanks!

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Question 189933: Hello.
Use completing the square to solve each equation:
x^2 - 4x + 30 = 0
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-4x%2B30 Start with the left side of the equation.


Take half of the x coefficient -4 to get -2. In other words, %281%2F2%29%28-4%29=-2.


Now square -2 to get 4. In other words, %28-2%29%5E2=%28-2%29%28-2%29=4


x%5E2-4x%2Bhighlight%284-4%29%2B30 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%5E2-4x%2B4%29-4%2B30 Group the first three terms.


%28x-2%29%5E2-4%2B30 Factor x%5E2-4x%2B4 to get %28x-2%29%5E2.


%28x-2%29%5E2%2B26 Combine like terms.


So after completing the square, x%5E2-4x%2B30 transforms to %28x-2%29%5E2%2B26. So x%5E2-4x%2B30=%28x-2%29%5E2%2B26.


So x%5E2-4x%2B30=0 is equivalent to %28x-2%29%5E2%2B26=0.


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%28x-2%29%5E2%2B26=0 Start with the given equation.


%28x-2%29%5E2=0-26Subtract 26 from both sides.


%28x-2%29%5E2=-26 Combine like terms.


x-2=0%2B-sqrt%28-26%29 Take the square root of both sides.


x-2=sqrt%28-26%29 or x-2=-sqrt%28-26%29 Break up the "plus/minus" to form two equations.


x-2=i%2Asqrt%2826%29 or x-2=-i%2Asqrt%2826%29 Simplify the square root. Note: i=sqrt%28-1%29


x=2%2Bi%2Asqrt%2826%29 or x=2-i%2Asqrt%2826%29 Add 2 to both sides.


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Answer:


So the solutions are x=2%2Bi%2Asqrt%2826%29 or x=2-i%2Asqrt%2826%29.