What is the answer to -8.4xi-3.15=-x^2 ?

The answer to -8.4xi-3.15=-x^2 is x=(3(14+sqrt(161)))/(10)i,x=(3(14-sqrt(161)))/(10)i

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-8.4xi-3.15=-x^2

- 8.4 x i - 3.15 = - x^{2}

x = \frac{3 ( 14 + 161 )}{10} i, x = \frac{3 ( 14 - 161 )}{10} i

Solution steps

- 8.4 x i - 3.15 = - x^{2}

Substitute

x = a + bi

- 8.4 (a + bi) i - 3.15 = - (a + bi)^{2}

Expand

(8.4 b - 3.15) - 8.4 ia = (- a^{2} + b^{2}) - 2 iab

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

[8.4 b - 3.15 = - a^{2} + b^{2} - 8.4 a = - 2 ab]

[8.4 b - 3.15 = - a^{2} + b^{2} - 8.4 a = - 2 ab] : a = 0, a = 0, b = \frac{3 ( 14 + 161 )}{10} b = \frac{3 ( 14 - 161 )}{10}

Substitute back

x = a + bi

x = \frac{3 ( 14 + 161 )}{10} i, x = \frac{3 ( 14 - 161 )}{10} i

i x = x^{2} - 2 x + 2

x^{2} + 2 x i + 1 = 0

(2 + i) 2 = c + d i

v = \frac{2 r}{i}

(x - y i)^{2} = 9 (x + y i)

What is the answer to -8.4xi-3.15=-x^2 ?
The answer to -8.4xi-3.15=-x^2 is x=(3(14+sqrt(161)))/(10)i,x=(3(14-sqrt(161)))/(10)i