Solve x 1/5(x-1)=1

Evaluate

x \times \frac{1}{5} (x - 1) = 1

Use the commutative property to reorder the terms

\frac{1}{5} x (x - 1) = 1

Expand the expression

More Steps

\frac{1}{5} x^{2} - \frac{1}{5} x = 1

Move the expression to the left side

\frac{1}{5} x^{2} - \frac{1}{5} x - 1 = 0

Multiply both sides

5 (\frac{1}{5} x^{2} - \frac{1}{5} x - 1) = 5 \times 0

Calculate

x^{2} - x - 5 = 0

Substitute a= 1,b= - 1 and c= - 5 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 \pm ( - 1 ) ^{2} - 4 ( - 5 )}{2}

Simplify the expression

More Steps

x = \frac{1 \pm 21}{2}

Separate the equation into 2 possible cases

x = \frac{1 + 21}{2} x = \frac{1 - 21}{2}

Solution

x_{1} = \frac{1 - 21}{2}, x_{2} = \frac{1 + 21}{2}

Alternative Form

x_{1} \approx - 1.791288, x_{2} \approx 2.791288

Solve the quadratic equation