Solve 4z^2+11z+3=-1

Evaluate

4 z^{2} + 11 z + 3 = - 1

Move the expression to the left side

4 z^{2} + 11 z + 4 = 0

Substitute a= 4,b= 11 and c= 4 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{- 11 \pm 1 1 ^{2} - 4 \times 4 \times 4}{2 \times 4}

Simplify the expression

z = \frac{- 11 \pm 1 1 ^{2} - 4 \times 4 \times 4}{8}

Simplify the expression

More Steps

z = \frac{- 11 \pm 57}{8}

Separate the equation into 2 possible cases

z = \frac{- 11 + 57}{8} z = \frac{- 11 - 57}{8}

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

z = \frac{- 11 + 57}{8} z = - \frac{11 + 57}{8}

Solution

z_{1} = - \frac{11 + 57}{8}, z_{2} = \frac{- 11 + 57}{8}

Alternative Form

z_{1} \approx - 2.318729, z_{2} \approx - 0.431271

4z^2+11z+3= 1