What are the solutions to the equation z^2-10z+45=5 ?

The solutions to the equation z^2-10z+45=5 are z=5+sqrt(15)i,z=5-sqrt(15)i

Find the zeros of z^2-10z+45=5

The zeros of z^2-10z+45=5 are z=5+sqrt(15)i,z=5-sqrt(15)i

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z^{2} - 10 z + 45 = 5

z = 5 + 15 i, z = 5 - 15 i

Solution steps

z^{2} - 10 z + 45 = 5

Move

5

to the left side

z^{2} - 10 z + 40 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 10 ) \pm ( - 10 ) ^{2} - 4 \cdot 1 \cdot 40}{2 \cdot 1}

Simplify

(- 10)^{2} - 4 \cdot 1 \cdot 40 : 215 i

z_{1, 2} = \frac{- ( - 10 ) \pm 2 15 i}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 10 ) + 2 15 i}{2 \cdot 1}, z_{2} = \frac{- ( - 10 ) - 2 15 i}{2 \cdot 1}

z = \frac{- ( - 10 ) + 2 15 i}{2 \cdot 1} : 5 + 15 i

z = \frac{- ( - 10 ) - 2 15 i}{2 \cdot 1} : 5 - 15 i

The solutions to the quadratic equation are:

z = 5 + 15 i, z = 5 - 15 i

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

- x^{2} + 9 x - 2 = 0

36 = 4 x^{2}

x^{2} + 36 = 100

x^{2} + \frac{3}{2} x = \frac{1}{4}

What are the solutions to the equation z^2-10z+45=5 ?
The solutions to the equation z^2-10z+45=5 are z=5+sqrt(15)i,z=5-sqrt(15)i
Find the zeros of z^2-10z+45=5
The zeros of z^2-10z+45=5 are z=5+sqrt(15)i,z=5-sqrt(15)i