Solve (1+x/3+x^2/10)

Question

Simplify the expression

\frac{30 + 10 x + 3 x ^{2}}{30}

Show Solution

x_{1} = - \frac{5}{3} - \frac{65}{3} i, x_{2} = - \frac{5}{3} + \frac{65}{3} i

Alternative Form

x_{1} \approx - 1. \dot{6} - 2.687419 i, x_{2} \approx - 1. \dot{6} + 2.687419 i

Evaluate

(1 + \frac{x}{3} + \frac{x ^{2}}{10})

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

1 + \frac{x}{3} + \frac{x ^{2}}{10} = 0

Add the terms

More Steps

\frac{30 + 10 x + 3 x ^{2}}{30} = 0

Simplify

30 + 10 x + 3 x^{2} = 0

Rewrite in standard form

3 x^{2} + 10 x + 30 = 0

Substitute a= 3,b= 10 and c= 30 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 10 \pm 1 0 ^{2} - 4 \times 3 \times 30}{2 \times 3}

Simplify the expression

x = \frac{- 10 \pm 1 0 ^{2} - 4 \times 3 \times 30}{6}

Simplify the expression

More Steps

x = \frac{- 10 \pm - 260}{6}

Simplify the radical expression

More Steps

x = \frac{- 10 \pm 2 65 \times i}{6}

Separate the equation into 2 possible cases

x = \frac{- 10 + 2 65 \times i}{6} x = \frac{- 10 - 2 65 \times i}{6}

Simplify the expression

More Steps

x = - \frac{5}{3} + \frac{65}{3} i x = \frac{- 10 - 2 65 \times i}{6}

Simplify the expression

More Steps

x = - \frac{5}{3} + \frac{65}{3} i x = - \frac{5}{3} - \frac{65}{3} i

Solution

x_{1} = - \frac{5}{3} - \frac{65}{3} i, x_{2} = - \frac{5}{3} + \frac{65}{3} i

Alternative Form

x_{1} \approx - 1. \dot{6} - 2.687419 i, x_{2} \approx - 1. \dot{6} + 2.687419 i

Show Solution