Solve Using the Square Root Property 6x^2-2x-3=0

Problem

6*x2−2*x−3=0

Solution

1. Isolate the constant term by adding 3 to both sides of the equation.

6*x2−2*x=3

2. Divide by the leading coefficient 6 to make the x2 coefficient equal to 1

x2−1/3*x=1/2

3. Complete the square by taking half of the xcoefficient, squaring it, and adding it to both sides.

Half of −1/3* is −1/6

(−1/6)2=1/36

x2−1/3*x+1/36=1/2+1/36

4. Simplify the right side by finding a common denominator.

1/2+1/36=18/36+1/36

18/36+1/36=19/36

5. Write the left side as a perfect square and set it equal to the simplified right side.

(x−1/6)2=19/36

6. Apply the Square Root Property by taking the square root of both sides and including the ± sign.

x−1/6=±√(,19/36)

x−1/6=±√(,19)/6

7. Solve for x by adding 1/6 to both sides.

x=1/6±√(,19)/6

x=(1±√(,19))/6

Final Answer

x=(1±√(,19))/6

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