What is ((-x^2)/(50))+10x-300>= 0 ?

The solution to ((-x^2)/(50))+10x-300>= 0 is -50sqrt(19)+250<= x<= 50sqrt(19)+250

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((-x^2)/(50))+10x-300>= 0

(\frac{- x ^{2}}{50}) + 10 x - 300 \geq 0

- 5019 + 250 \leq x \leq 5019 + 250

Interval Notation

[- 5019 + 250, 5019 + 250]

Decimal Notation

32.05505 \dots \leq x \leq 467.94494 \dots

Solution steps

\frac{- x ^{2}}{50} + 10 x - 300 \geq 0

Rewrite in standard form

- x^{2} + 500 x - 15000 \geq 0

Complete the square

- x^{2} + 500 x - 15000 : - (x - 250)^{2} + 47500

- (x - 250)^{2} + 47500 \geq 0

Move

47500

to the right side

- (x - 250)^{2} \geq - 47500

Multiply both sides by

- 1

(x - 250)^{2} \leq 47500

For

u^{n} \leq a

, if

n

is even then

- 47500 \leq x - 250 \leq 47500

a \leq u \leq b

then

a \leq u and u \leq b

- 47500 \leq x - 250 and x - 250 \leq 47500

- 47500 \leq x - 250 : x \geq - 5019 + 250

x - 250 \leq 47500 : x \leq 5019 + 250

Combine the intervals

x \geq - 5019 + 250 and x \leq 5019 + 250

Merge Overlapping Intervals

- 5019 + 250 \leq x \leq 5019 + 250

9 x \leq - 36

x^{2} + 8 x + 2 = 0

440

64 x^{6} - 1

- 2 - 4

What is ((-x^2)/(50))+10x-300>= 0 ?
The solution to ((-x^2)/(50))+10x-300>= 0 is -50sqrt(19)+250<= x<= 50sqrt(19)+250