SOLUTION: Can you please help show me how to solve this quadratic equation by completing the square w^2 - 5w = 14

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Question 169986: Can you please help show me how to solve this quadratic equation by completing the square
w^2 - 5w = 14
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
w%5E2-5w=14 Start with the given equation.


Take half of the "w" coefficient -5 to get -5%2F2. Now square -5%2F2 to get %28-5%2F2%29%5E2=25%2F4. Add this value to both sides


w%5E2-5w%2B25%2F4=14%2B25%2F4 Add 25%2F4 to both sides


w%5E2-5w%2B25%2F4=81%2F4 Combine like terms.


4w%5E2-4%285w%29%2Bcross%284%29%2825%2Fcross%284%29%29=cross%284%29%2881%2Fcross%284%29%29 Multiply EVERY term by the LCD 4 to clear the fractions


4w%5E2-20w%2B25=81 Multiply and simplify


%282w-5%29%5E2=81 Factor 4w%5E2-20w%2B25 to get %282w-5%29%5E2


2w-5=0%2B-sqrt%2881%29 Take the square root of both sides


2w-5=9 or 2w-5=-9 Break up the "plus/minus" to form two equations


2w-5=sqrt%2881%29 or 2w-5=-sqrt%2881%29 Take the square root of 81 to get 9


2w=5%2B9 or 2w=5-9 Add 5 to both sides


2w=14 or 2w=-4 Combine like terms.


w=14%2F2 or w=-4%2F2 Divide both sides by 2 to isolate "w"


w=7 or w=-2 Divide


So the answers are w+=+7 or w+=+-2