What is the answer to i=-5x^2+10x+10 ?

The answer to i=-5x^2+10x+10 is x=-0.73301…+0.05770…i,x=2.73301…-0.05770…i

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i=-5x^2+10x+10

i = - 5 x^{2} + 10 x + 10

x = - 0.73301 \dots + 0.05770 \dots i, x = 2.73301 \dots - 0.05770 \dots i

Solution steps

i = - 5 x^{2} + 10 x + 10

Substitute

x = a + bi

i = - 5 (a + bi)^{2} + 10 (a + bi) + 10

Expand

- 5 (a + bi)^{2} + 10 (a + bi) + 10 : (- 5 a^{2} + 5 b^{2} + 10 a + 10) + i (10 b - 10 ab)

i = (- 5 a^{2} + 5 b^{2} + 10 a + 10) + i (10 b - 10 ab)

Rewrite

i

in standard complex form:

0 + i

0 + i = (- 5 a^{2} + 5 b^{2} + 10 a + 10) + i (10 b - 10 ab)

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

[0 = - 5 a^{2} + 5 b^{2} + 10 a + 10 1 = 10 b - 10 ab]

[0 = - 5 a^{2} + 5 b^{2} + 10 a + 10 1 = 10 b - 10 ab] : (a = - 0.73301 \dots, a = 2.73301 \dots, b = 0.05770 \dots b = - 0.05770 \dots)

Substitute back

x = a + bi

x = - 0.73301 \dots + 0.05770 \dots i, x = 2.73301 \dots - 0.05770 \dots i

M = C (1 + i t)

∣ z ∣ - z = 1 + 0 i

x, z = x^{2} + i

3 (5 + bi) + 2 i = 2 a - 7 i

s i P (x) = 2 x - 1, Q (x) = x + 3

What is the answer to i=-5x^2+10x+10 ?
The answer to i=-5x^2+10x+10 is x=-0.73301…+0.05770…i,x=2.73301…-0.05770…i