Solve (x 1) / 3 (x - 2) / 2 = 3

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 1 - 19, x_{2} = 1 + 19

Alternative Form

x_{1} \approx - 3.358899, x_{2} \approx 5.358899

Evaluate

\frac{x \times 1}{3} \times \frac{x - 2}{2} = 3

Simplify

More Steps

\frac{x ( x - 2 )}{6} = 3

Rewrite the expression

\frac{1}{6} x^{2} - \frac{1}{3} x = 3

Move the expression to the left side

\frac{1}{6} x^{2} - \frac{1}{3} x - 3 = 0

Multiply both sides

6 (\frac{1}{6} x^{2} - \frac{1}{3} x - 3) = 6 \times 0

Calculate

x^{2} - 2 x - 18 = 0

Substitute a= 1,b= - 2 and c= - 18 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 ( - 18 )}{2}

Simplify the expression

More Steps

x = \frac{2 \pm 76}{2}

Simplify the radical expression

More Steps

x = \frac{2 \pm 2 19}{2}

Separate the equation into 2 possible cases

x = \frac{2 + 2 19}{2} x = \frac{2 - 2 19}{2}

Simplify the expression

More Steps

x = 1 + 19 x = \frac{2 - 2 19}{2}

Simplify the expression

More Steps

x = 1 + 19 x = 1 - 19

Solution

x_{1} = 1 - 19, x_{2} = 1 + 19

Alternative Form

x_{1} \approx - 3.358899, x_{2} \approx 5.358899

Show Solution