Solve 2t^2-t-1=0 - ScanMath

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

t_{1} = - 0.5, t_{2} = 1

Evaluate

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

Factor the expression

More Steps

Evaluate

2 t^{2} - t - 1

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out t from the expression

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

Factor out - 1 from the expression

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

Factor out 2 t + 1 from the expression

(t - 1) (2 t + 1)

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

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

t - 1 = 0 2 t + 1 = 0

Solve the equation for t

More Steps

Evaluate

t - 1 = 0

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

t = 0 + 1

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

t = 1

t = 1 2 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}

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

t = - \frac{1}{2}

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

Solution

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

Alternative Form

t_{1} = - 0.5, t_{2} = 1

Show Solution