What are the solutions to the equation z^2-16z+61=2z*20 ?

The solutions to the equation z^2-16z+61=2z*20 are z=28+sqrt(723),z=28-sqrt(723)

Find the zeros of z^2-16z+61=2z*20

The zeros of z^2-16z+61=2z*20 are z=28+sqrt(723),z=28-sqrt(723)

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z^{2} - 16 z + 61 = 2 z \cdot 20

z = 28 + 723, z = 28 - 723

Decimal Notation

z = 54.88865 \dots, z = 1.11134 \dots

Solution steps

z^{2} - 16 z + 61 = 2 z \cdot 20

Expand

2 z \cdot 20 : 40 z

z^{2} - 16 z + 61 = 40 z

Move

40 z

to the left side

z^{2} - 56 z + 61 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 56 ) \pm ( - 56 ) ^{2} - 4 \cdot 1 \cdot 61}{2 \cdot 1}

(- 56)^{2} - 4 \cdot 1 \cdot 61 = 2723

z_{1, 2} = \frac{- ( - 56 ) \pm 2 723}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 56 ) + 2 723}{2 \cdot 1}, z_{2} = \frac{- ( - 56 ) - 2 723}{2 \cdot 1}

z = \frac{- ( - 56 ) + 2 723}{2 \cdot 1} : 28 + 723

z = \frac{- ( - 56 ) - 2 723}{2 \cdot 1} : 28 - 723

The solutions to the quadratic equation are:

z = 28 + 723, z = 28 - 723

x^{2} - 4 x - 15 = 18

x^{2} = 2 a^{2}

9 x^{2} - 36 + 32

18 x^{2} - 12 m x + (6 m - 2) = 0

b^{2} - 12 b - 9 = 8

What are the solutions to the equation z^2-16z+61=2z*20 ?
The solutions to the equation z^2-16z+61=2z*20 are z=28+sqrt(723),z=28-sqrt(723)
Find the zeros of z^2-16z+61=2z*20
The zeros of z^2-16z+61=2z*20 are z=28+sqrt(723),z=28-sqrt(723)