What are the solutions to the equation 4z^2+11z+3=-1 ?

The solutions to the equation 4z^2+11z+3=-1 are z=(-11+sqrt(57))/8 ,z=(-11-sqrt(57))/8

Find the zeros of 4z^2+11z+3=-1

The zeros of 4z^2+11z+3=-1 are z=(-11+sqrt(57))/8 ,z=(-11-sqrt(57))/8

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

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

Decimal Notation

z = - 0.43127 \dots, z = - 2.31872 \dots

Solution steps

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

Move

1

to the left side

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

Solve with the quadratic formula

z_{1, 2} = \frac{- 11 \pm 1 1 ^{2} - 4 \cdot 4 \cdot 4}{2 \cdot 4}

1 1^{2} - 4 \cdot 4 \cdot 4 = 57

z_{1, 2} = \frac{- 11 \pm 57}{2 \cdot 4}

Separate the solutions

z_{1} = \frac{- 11 + 57}{2 \cdot 4}, z_{2} = \frac{- 11 - 57}{2 \cdot 4}

z = \frac{- 11 + 57}{2 \cdot 4} : \frac{- 11 + 57}{8}

z = \frac{- 11 - 57}{2 \cdot 4} : \frac{- 11 - 57}{8}

The solutions to the quadratic equation are:

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

9 u^{2} + 25 = - 30 u

x^{2} + 5 x + \frac{9}{4}

5 y^{2} + 7 y - 1 = 0

x, x^{2} + y^{2} + z^{2} = 16

2 x^{2} - 3 x - 15 = - 4 x

What are the solutions to the equation 4z^2+11z+3=-1 ?
The solutions to the equation 4z^2+11z+3=-1 are z=(-11+sqrt(57))/8 ,z=(-11-sqrt(57))/8
Find the zeros of 4z^2+11z+3=-1
The zeros of 4z^2+11z+3=-1 are z=(-11+sqrt(57))/8 ,z=(-11-sqrt(57))/8