Solve 7-t -6t^2t - ScanMath

Question

Simplify the expression

7 - t - 6 t^{3}

Evaluate

7 - t - 6 t^{2} \times t

Solution

More Steps

Evaluate

- 6 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 6 t^{2 + 1}

Add the numbers

- 6 t^{3}

7 - t - 6 t^{3}

Show Solution

Factor the expression

(1 - t) (6 t^{2} + 6 t + 7)

Evaluate

7 - t - 6 t^{2} \times t

Multiply

More Steps

Evaluate

6 t^{2} \times t

Multiply the terms with the same base by adding their exponents

6 t^{2 + 1}

Add the numbers

6 t^{3}

7 - t - 6 t^{3}

Calculate

6 t^{2} + 6 t + 7 - 6 t^{3} - 6 t^{2} - 7 t

Rewrite the expression

6 t^{2} + 6 t + 7 - t \times 6 t^{2} - t \times 6 t - t \times 7

Factor out - t from the expression

6 t^{2} + 6 t + 7 - t (6 t^{2} + 6 t + 7)

Solution

(1 - t) (6 t^{2} + 6 t + 7)

Show Solution

Find the roots

t_{1} = - \frac{1}{2} - \frac{33}{6} i, t_{2} = - \frac{1}{2} + \frac{33}{6} i, t_{3} = 1

Alternative Form

t_{1} \approx - 0.5 - 0.957427 i, t_{2} \approx - 0.5 + 0.957427 i, t_{3} = 1

Evaluate

7 - t - 6 t^{2} \times t

To find the roots of the expression,set the expression equal to 0

7 - t - 6 t^{2} \times t = 0

Multiply

More Steps

Multiply the terms

6 t^{2} \times t

Multiply the terms with the same base by adding their exponents

6 t^{2 + 1}

Add the numbers

6 t^{3}

7 - t - 6 t^{3} = 0

Factor the expression

(1 - t) (6 t^{2} + 6 t + 7) = 0

Separate the equation into 2 possible cases

1 - t = 0 6 t^{2} + 6 t + 7 = 0

Solve the equation

More Steps

Evaluate

1 - t = 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

Change the signs on both sides of the equation

t = 1

t = 1 6 t^{2} + 6 t + 7 = 0

Solve the equation

More Steps

Evaluate

6 t^{2} + 6 t + 7 = 0

Substitute a= 6,b= 6 and c= 7 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{- 6 \pm 6 ^{2} - 4 \times 6 \times 7}{2 \times 6}

Simplify the expression

t = \frac{- 6 \pm 6 ^{2} - 4 \times 6 \times 7}{12}

Simplify the expression

More Steps

Evaluate

6^{2} - 4 \times 6 \times 7

Multiply the terms

6^{2} - 168

Evaluate the power

36 - 168

Subtract the numbers

- 132

t = \frac{- 6 \pm - 132}{12}

Simplify the radical expression

More Steps

Evaluate

- 132

Evaluate the power

132 \times - 1

Evaluate the power

132 \times i

Evaluate the power

233 \times i

t = \frac{- 6 \pm 2 33 \times i}{12}

Separate the equation into 2 possible cases

t = \frac{- 6 + 2 33 \times i}{12} t = \frac{- 6 - 2 33 \times i}{12}

Simplify the expression

t = - \frac{1}{2} + \frac{33}{6} i t = \frac{- 6 - 2 33 \times i}{12}

Simplify the expression

t = - \frac{1}{2} + \frac{33}{6} i t = - \frac{1}{2} - \frac{33}{6} i

t = 1 t = - \frac{1}{2} + \frac{33}{6} i t = - \frac{1}{2} - \frac{33}{6} i

Solution

t_{1} = - \frac{1}{2} - \frac{33}{6} i, t_{2} = - \frac{1}{2} + \frac{33}{6} i, t_{3} = 1

Alternative Form

t_{1} \approx - 0.5 - 0.957427 i, t_{2} \approx - 0.5 + 0.957427 i, t_{3} = 1

Show Solution