What is -0.01x^2+0.04x<x+3 ?

The solution to -0.01x^2+0.04x 2sqrt(501)-48

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-0.01x^2+0.04x<x+3

- 0.01 x^{2} + 0.04 x < x + 3

x < - 2501 - 48 or x > 2501 - 48

Interval Notation

(- \infty, - 2501 - 48) \cup (2501 - 48, \infty)

Decimal Notation

x < - 92.76605 \dots or x > - 3.23394 \dots

Solution steps

- 0.01 x^{2} + 0.04 x < x + 3

Rewrite in standard form

- 0.01 x^{2} - 0.96 x - 3 < 0

Complete the square

- 0.01 x^{2} - 0.96 x - 3 : - 0.01 (x + 48)^{2} + 20.04

- 0.01 (x + 48)^{2} + 20.04 < 0

Multiply both sides by

100

- (x + 48)^{2} + 2004 < 0

Move

2004

to the right side

- (x + 48)^{2} < - 2004

Multiply both sides by

- 1

(x + 48)^{2} > 2004

For

u^{n} > a

, if

n

is even then

x + 48 < - 2004 or x + 48 > 2004

x + 48 < - 2004 : x < - 2501 - 48

x + 48 > 2004 : x > 2501 - 48

Combine the intervals

x < - 2501 - 48 or x > 2501 - 48

(3 x - 3)^{2} = 23

12 = - 4 (- 6 x - 3)

c^{2} + 5 c = 36

∣ u - 7 ∣ = 1

x^{2} = 10 x

What is -0.01x^2+0.04x<x+3 ?
The solution to -0.01x^2+0.04x<x+3 is x<-2sqrt(501)-48\lor x>2sqrt(501)-48