SOLUTION: Please help me solve this equation: x^2+3/5x-1=0 It is called completing the square and has to do with solving quadratic equations.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this equation: x^2+3/5x-1=0 It is called completing the square and has to do with solving quadratic equations.      Log On


   

Question 196864This question is from textbook McDougal Littell Algebra 1
: Please help me solve this equation: x^2+3/5x-1=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!
First, let's complete the square:


x%5E2%2B%283%2F5%29x-1 Start with the left side of the given equation.


Take half of the x coefficient 3%2F5 to get 3%2F10. In other words, %281%2F2%29%283%2F5%29=3%2F10.


Now square 3%2F10 to get 9%2F100. In other words, %283%2F10%29%5E2=%283%2F10%29%283%2F10%29=9%2F100


x%5E2%2B%283%2F5%29x%2Bhighlight%289%2F100-9%2F100%29-1 Now add and subtract 9%2F100. Make sure to place this after the "x" term. Notice how 9%2F100-9%2F100=0. So the expression is not changed.


%28x%5E2%2B%283%2F5%29x%2B9%2F100%29-9%2F100-1 Group the first three terms.


%28x%2B3%2F10%29%5E2-9%2F100-1 Factor x%5E2%2B%283%2F5%29x%2B9%2F100 to get %28x%2B3%2F10%29%5E2.


%28x%2B3%2F10%29%5E2-109%2F100 Combine like terms.


So after completing the square, x%5E2%2B3%2F5x-1 transforms to %28x%2B3%2F10%29%5E2-109%2F100. So x%5E2%2B3%2F5x-1=%28x%2B3%2F10%29%5E2-109%2F100.


So x%5E2%2B%283%2F5%29x-1=0 is equivalent to %28x%2B3%2F10%29%5E2-109%2F100=0.


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Now let's solve %28x%2B3%2F10%29%5E2-109%2F100=0


%28x%2B3%2F10%29%5E2-109%2F100=0 Start with the given equation.


%28x%2B3%2F10%29%5E2=0%2B109%2F100Add 109%2F100 to both sides.


%28x%2B3%2F10%29%5E2=109%2F100 Combine like terms.


x%2B3%2F10=0%2B-sqrt%28109%2F100%29 Take the square root of both sides.


x%2B3%2F10=sqrt%28109%2F100%29 or x%2B3%2F10=-sqrt%28109%2F100%29 Break up the "plus/minus" to form two equations.


x%2B3%2F10=sqrt%28109%29%2F10 or x%2B3%2F10=-sqrt%28109%29%2F10 Simplify the square root.


x=-3%2F10%2Bsqrt%28109%29%2F10 or x=-3%2F10-sqrt%28109%29%2F10 Subtract 3%2F10 from both sides.


x=%28-3%2Bsqrt%28109%29%29%2F%2810%29 or x=%28-3-sqrt%28109%29%29%2F%2810%29 Combine the fractions.


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Answer:


So the solutions are x=%28-3%2Bsqrt%28109%29%29%2F%2810%29 or x=%28-3-sqrt%28109%29%29%2F%2810%29.