SOLUTION: 4x^2+2x-3=0. Solve by completing the square. (4x^2 is 4x squared)

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Question 101192: 4x^2+2x-3=0. Solve by completing the square. (4x^2 is 4x squared)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2%2B2x-3=0 Start with the given equation


4x%5E2%2B2x=3 Add 3 to both sides
4%28x%5E2%2B0.5x%29=3 Factor out the leading coefficient 4. This step is important since we want the x%5E2 coefficient to be equal to 1.



Take half of the x coefficient 0.5 to get 0.25 (ie 0.5%2F2=0.25)
Now square 0.25 to get 0.0625 (ie %280.25%29%5E2=0.0625)



4%28x%5E2%2B0.5x%2B0.0625%29=3%2B0.0625%284%29 Add this result (0.0625) to the expression x%5E2%2B0.5x inside the parenthesis. Now the expression x%5E2%2B0.5x%2B0.0625 is a perfect square trinomial. Now add the result (0.0625)(4) (remember we factored out a 4) to the right side.



4%28x%2B0.25%29%5E2=3%2B0.0625%284%29 Factor x%5E2%2B0.5x%2B0.0625 into %28x%2B0.25%29%5E2


4%28x%2B0.25%29%5E2=3%2B0.25 Multiply 0.0625 and 4 to get 0.25



4%28x%2B0.25%29%5E2=3.25 Combine like terms on the right side

%28x%2B0.25%29%5E2=0.8125 Divide both sides by 4


x%2B0.25=0%2B-sqrt%280.8125%29 Take the square root of both sides

x=-0.25%2B-sqrt%280.8125%29 Subtract 0.25 from both sides to isolate x.

So the expression breaks down to
x=-0.25%2Bsqrt%280.8125%29 or x=-0.25-sqrt%280.8125%29


So our answer is approximately
x=0.651387818865997 or x=-1.151387818866

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+4x%5E2%2B2x-3%29+ graph of y=4x%5E2%2B2x-3


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=0.651387818865997 and x=-1.151387818866, so this verifies our answer.