Solve 6t^2-t-1 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

t_{1} = - \frac{1}{3}, t_{2} = \frac{1}{2}

Alternative Form

t_{1} = - 0. \dot{3}, t_{2} = 0.5

Evaluate

6 t^{2} - t - 1 = 0

Factor the expression

More Steps

Evaluate

6 t^{2} - t - 1

Rewrite the expression

6 t^{2} + (2 - 3) t - 1

Calculate

6 t^{2} + 2 t - 3 t - 1

Rewrite the expression

2 t \times 3 t + 2 t - 3 t - 1

Factor out 2 t from the expression

2 t (3 t + 1) - 3 t - 1

Factor out - 1 from the expression

2 t (3 t + 1) - (3 t + 1)

Factor out 3 t + 1 from the expression

(2 t - 1) (3 t + 1)

(2 t - 1) (3 t + 1) = 0

When the product of factors equals 0,at least one factor is 0

2 t - 1 = 0 3 t + 1 = 0

Solve the equation for t

More Steps

Evaluate

2 t - 1 = 0

Move the constant to the right-hand side and change its sign

2 t = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

2 t = 1

Divide both sides

\frac{2 t}{2} = \frac{1}{2}

Divide the numbers

t = \frac{1}{2}

t = \frac{1}{2} 3 t + 1 = 0

Solve the equation for t

More Steps

Evaluate

3 t + 1 = 0

Move the constant to the right-hand side and change its sign

3 t = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

3 t = - 1

Divide both sides

\frac{3 t}{3} = \frac{- 1}{3}

Divide the numbers

t = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

t = - \frac{1}{3}

t = \frac{1}{2} t = - \frac{1}{3}

Solution

t_{1} = - \frac{1}{3}, t_{2} = \frac{1}{2}

Alternative Form

t_{1} = - 0. \dot{3}, t_{2} = 0.5

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