Solve Using the Quadratic Formula 1/6x^2-1/3x=1

Problem

1/6*x2−1/3*x=1

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by subtracting 1 from both sides.

1/6*x2−1/3*x−1=0

2. Clear the fractions by multiplying the entire equation by the least common denominator, which is 6

x2−2*x−6=0

3. Identify the coefficients a b and c for use in the quadratic formula.

a=1

b=−2

c=−6

4. Substitute the coefficients into the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−2)±√(,(−2)2−4*(1)*(−6)))/(2*(1))

5. Simplify the expression under the radical (the discriminant).

x=(2±√(,4+24))/2

x=(2±√(,28))/2

6. Simplify the square root by factoring out the largest perfect square.

x=(2±2√(,7))/2

7. Divide both terms in the numerator by the denominator to find the final values of x

x=1±√(,7)

Final Answer

1/6*x2−1/3*x=1⇒x=1±√(,7)

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