SOLUTION: Please show me how to work out this quadratic equation by completing the square m^2 = 8m + 3

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Question 170121: Please show me how to work out this quadratic equation by completing the square
m^2 = 8m + 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
m%5E2=8m%2B3 Start with the given equation.


m%5E2-8m-3=0 Get all terms to the left side.


Now let's complete the square:


m%5E2-8m-3 Start with the left side of the equation.


Take half of the m coefficient -8 to get -4. In other words, %281%2F2%29%28-8%29=-4.


Now square -4 to get 16. In other words, %28-4%29%5E2=%28-4%29%28-4%29=16


m%5E2-8m%2Bhighlight%2816-16%29-3 Now add and subtract 16. Make sure to place this after the "m" term. Notice how 16-16=0. So the expression is not changed.


%28m%5E2-8m%2B16%29-16-3 Group the first three terms.


%28m-4%29%5E2-16-3 Factor m%5E2-8m%2B16 to get %28m-4%29%5E2.


%28m-4%29%5E2-19 Combine like terms.


So after completing the square, m%5E2-8m-3 transforms to %28m-4%29%5E2-19. So m%5E2-8m-3=%28m-4%29%5E2-19.


So m%5E2-8m-3=0 is equivalent to %28m-4%29%5E2-19=0.


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%28m-4%29%5E2-19=0 Start with the given equation.


%28m-4%29%5E2=0%2B19Add 19 to both sides.


%28m-4%29%5E2=19 Combine like terms.


x-4=0%2B-sqrt%2819%29 Take the square root of both sides.


m-4=sqrt%2819%29 or m-4=-sqrt%2819%29 Break up the "plus/minus" to form two equations.


m=4%2Bsqrt%2819%29 or m=4-sqrt%2819%29 Add 4 to both sides.


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Answer:


So the solutions are m=4%2Bsqrt%2819%29 or m=4-sqrt%2819%29


which approximate to m=8.359 or m=-0.359