Solve 1/9 (x- 1/3 )^(2)= 5/9

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{1 - 3 5}{3}, x_{2} = \frac{1 + 3 5}{3}

Alternative Form

x_{1} \approx - 1.902735, x_{2} \approx 2.569401

Evaluate

\frac{1}{9} (x - \frac{1}{3})^{2} = \frac{5}{9}

Expand the expression

More Steps

\frac{1}{9} x^{2} - \frac{2}{27} x + \frac{1}{81} = \frac{5}{9}

Move the expression to the left side

\frac{1}{9} x^{2} - \frac{2}{27} x - \frac{44}{81} = 0

Multiply both sides

81 (\frac{1}{9} x^{2} - \frac{2}{27} x - \frac{44}{81}) = 81 \times 0

Calculate

9 x^{2} - 6 x - 44 = 0

Substitute a= 9,b= - 6 and c= - 44 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 9 ( - 44 )}{2 \times 9}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 9 ( - 44 )}{18}

Simplify the expression

More Steps

x = \frac{6 \pm 1620}{18}

Simplify the radical expression

More Steps

x = \frac{6 \pm 18 5}{18}

Separate the equation into 2 possible cases

x = \frac{6 + 18 5}{18} x = \frac{6 - 18 5}{18}

Simplify the expression

More Steps

x = \frac{1 + 3 5}{3} x = \frac{6 - 18 5}{18}

Simplify the expression

More Steps

x = \frac{1 + 3 5}{3} x = \frac{1 - 3 5}{3}

Solution

x_{1} = \frac{1 - 3 5}{3}, x_{2} = \frac{1 + 3 5}{3}

Alternative Form

x_{1} \approx - 1.902735, x_{2} \approx 2.569401

Show Solution