What is the answer to i(x)=-x^2+80x+650 ?

The answer to i(x)=-x^2+80x+650 is x=-7.43340…-0.07835…i,x=87.43340…-0.92164…i

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i(x)=-x^2+80x+650

i (x) = - x^{2} + 80 x + 650

x = - 7.43340 \dots - 0.07835 \dots i, x = 87.43340 \dots - 0.92164 \dots i

Solution steps

i (x) = - x^{2} + 80 x + 650

Substitute

x = a + bi

i (a + bi) = - (a + bi)^{2} + 80 (a + bi) + 650

Expand

- b + ia = (- a^{2} + b^{2} + 80 a + 650) + i (80 b - 2 ab)

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

[- b = - a^{2} + b^{2} + 80 a + 650 a = 80 b - 2 ab]

[- b = - a^{2} + b^{2} + 80 a + 650 a = 80 b - 2 ab] : (a = - 7.43340 \dots, a = 87.43340 \dots, b = - 0.07835 \dots b = - 0.92164 \dots)

Substitute back

x = a + bi

x = - 7.43340 \dots - 0.07835 \dots i, x = 87.43340 \dots - 0.92164 \dots i

(1 + i) (x + 2 y) + (3 - 2 i) (x - y) = 8 + 3 i 3 i

3 x + (y - x) i = 6

z^{2} + 2 - 23 i = 0

4 x_{1} + 5 x_{2} = (1 + i) x_{1}

z^{2} - z - 1 + i = 0

What is the answer to i(x)=-x^2+80x+650 ?
The answer to i(x)=-x^2+80x+650 is x=-7.43340…-0.07835…i,x=87.43340…-0.92164…i