SOLUTION: Please help me solve this equation: x^2+5x-11/4=0 It is called "completing the square" and has to do with solving quadratic equations.

Algebra ->  Square-cubic-other-roots -> SOLUTION: Please help me solve this equation: x^2+5x-11/4=0 It is called "completing the square" and has to do with solving quadratic equations.      Log On


   

Question 196845This question is from textbook McDougal Littell Algebra 1
: Please help me solve this equation: x^2+5x-11/4=0
It is called "completing the square" and has to do with solving quadratic equations. This question is from textbook McDougal Littell Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this, let's first complete the square:


x%5E2%2B5x-11%2F4 Start with the left side of the given equation.


Take half of the x coefficient 5 to get 5%2F2. In other words, %281%2F2%29%285%29=5%2F2.


Now square 5%2F2 to get 25%2F4. In other words, %285%2F2%29%5E2=%285%2F2%29%285%2F2%29=25%2F4


x%5E2%2B5x%2Bhighlight%2825%2F4-25%2F4%29-11%2F4 Now add and subtract 25%2F4. Make sure to place this after the "x" term. Notice how 25%2F4-25%2F4=0. So the expression is not changed.


%28x%5E2%2B5x%2B25%2F4%29-25%2F4-11%2F4 Group the first three terms.


%28x%2B5%2F2%29%5E2-25%2F4-11%2F4 Factor x%5E2%2B5x%2B25%2F4 to get %28x%2B5%2F2%29%5E2.


%28x%2B5%2F2%29%5E2-9 Combine like terms.


So after completing the square, x%5E2%2B5x-11%2F4 transforms to %28x%2B5%2F2%29%5E2-9. So x%5E2%2B5x-11%2F4=%28x%2B5%2F2%29%5E2-9.


So x%5E2%2B5x-11%2F4=0 is equivalent to %28x%2B5%2F2%29%5E2-9=0.



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Now let's solve %28x%2B5%2F2%29%5E2-9=0


%28x%2B5%2F2%29%5E2-9=0 Start with the given equation.


%28x%2B5%2F2%29%5E2=0%2B9Add 9 to both sides.


%28x%2B5%2F2%29%5E2=9 Combine like terms.


x%2B5%2F2=%22%22%2B-sqrt%289%29 Take the square root of both sides.


x%2B5%2F2=sqrt%289%29 or x%2B5%2F2=-sqrt%289%29 Break up the "plus/minus" to form two equations.


x%2B5%2F2=3 or x%2B5%2F2=-3 Take the square root of 9 to get 3.


x=-5%2F2%2B3 or x=-5%2F2-3 Subtract 5%2F2 from both sides.


x=1%2F2 or x=-11%2F2 Combine like terms.


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Answer:


So the solutions are x=1%2F2 or x=-11%2F2.