What are the solutions to the equation 2z^2+2.5z+3.75=0 ?

The solutions to the equation 2z^2+2.5z+3.75=0 are z=-5/8+i(sqrt(95))/8 ,z=-5/8-i(sqrt(95))/8

Find the zeros of 2z^2+2.5z+3.75=0

The zeros of 2z^2+2.5z+3.75=0 are z=-5/8+i(sqrt(95))/8 ,z=-5/8-i(sqrt(95))/8

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2 z^{2} + 2.5 z + 3.75 = 0

z = - \frac{5}{8} + i \frac{95}{8}, z = - \frac{5}{8} - i \frac{95}{8}

Solution steps

2 z^{2} + 2.5 z + 3.75 = 0

Multiply both sides by

100

200 z^{2} + 250 z + 375 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- 250 \pm 25 0 ^{2} - 4 \cdot 200 \cdot 375}{2 \cdot 200}

Simplify

25 0^{2} - 4 \cdot 200 \cdot 375 : 5095 i

z_{1, 2} = \frac{- 250 \pm 50 95 i}{2 \cdot 200}

Separate the solutions

z_{1} = \frac{- 250 + 50 95 i}{2 \cdot 200}, z_{2} = \frac{- 250 - 50 95 i}{2 \cdot 200}

z = \frac{- 250 + 50 95 i}{2 \cdot 200} : - \frac{5}{8} + i \frac{95}{8}

z = \frac{- 250 - 50 95 i}{2 \cdot 200} : - \frac{5}{8} - i \frac{95}{8}

The solutions to the quadratic equation are:

z = - \frac{5}{8} + i \frac{95}{8}, z = - \frac{5}{8} - i \frac{95}{8}

6 x^{2} = 29 x + 5

2 x (x - 3) = x^{2} - 9

- x^{2} + 6 x + 3 = x + 3

4 x^{2} + x + 12 = 0

5 x^{2} - 37 x - 24 = 0

What are the solutions to the equation 2z^2+2.5z+3.75=0 ?
The solutions to the equation 2z^2+2.5z+3.75=0 are z=-5/8+i(sqrt(95))/8 ,z=-5/8-i(sqrt(95))/8
Find the zeros of 2z^2+2.5z+3.75=0
The zeros of 2z^2+2.5z+3.75=0 are z=-5/8+i(sqrt(95))/8 ,z=-5/8-i(sqrt(95))/8