What is the answer to 2x^2=14x-30i ?

The answer to 2x^2=14x-30i is x=-0.47596…+1.88633…i,x=7.47596…-1.88633…i

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2x^2=14x-30i

2 x^{2} = 14 x - 30 i

x = - 0.47596 \dots + 1.88633 \dots i, x = 7.47596 \dots - 1.88633 \dots i

Solution steps

2 x^{2} = 14 x - 30 i

Substitute

x = a + bi

2 (a + bi)^{2} = 14 (a + bi) - 30 i

Expand

(2 a^{2} - 2 b^{2}) + 4 iab = 14 a + i (- 30 + 14 b)

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[2 a^{2} - 2 b^{2} = 14 a 4 ab = - 30 + 14 b]

[2 a^{2} - 2 b^{2} = 14 a 4 ab = - 30 + 14 b] : (a = - 0.47596 \dots, a = 7.47596 \dots, b = 1.88633 \dots b = - 1.88633 \dots)

Substitute back

x = a + bi

x = - 0.47596 \dots + 1.88633 \dots i, x = 7.47596 \dots - 1.88633 \dots i

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3 z^{2} + (2 - 3 i) z - 1 - 3 i = 0

r (t) = (2 t + 1) i + (t^{2} - 1) j

2 x + 51 = 4 (2 + y i) - 12

z^{2} - (1 + 9 i) z - 20 + 5 i = 0

What is the answer to 2x^2=14x-30i ?
The answer to 2x^2=14x-30i is x=-0.47596…+1.88633…i,x=7.47596…-1.88633…i