What is x^2-30x+150<= 0 ?

The solution to x^2-30x+150<= 0 is -5sqrt(3)+15<= x<= 5sqrt(3)+15

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x^2-30x+150<= 0

x^{2} - 30 x + 150 \leq 0

- 53 + 15 \leq x \leq 53 + 15

Interval Notation

[- 53 + 15, 53 + 15]

Decimal Notation

6.33974 \dots \leq x \leq 23.66025 \dots

Solution steps

x^{2} - 30 x + 150 \leq 0

Complete the square

x^{2} - 30 x + 150 : (x - 15)^{2} - 75

(x - 15)^{2} - 75 \leq 0

Move

75

to the right side

(x - 15)^{2} \leq 75

For

u^{n} \leq a

, if

n

is even then

- 75 \leq x - 15 \leq 75

a \leq u \leq b

then

a \leq u and u \leq b

- 75 \leq x - 15 and x - 15 \leq 75

- 75 \leq x - 15 : x \geq - 53 + 15

x - 15 \leq 75 : x \leq 53 + 15

Combine the intervals

x \geq - 53 + 15 and x \leq 53 + 15

Merge Overlapping Intervals

- 53 + 15 \leq x \leq 53 + 15

2 x^{2} - 3 = 253

C a (s) + M g C l^{2} (a p)

80 - x + 145 = 135

ln (2) e^{l n (2)}

3 (x - 1)^{2} = (2 x + 5)

What is x^2-30x+150<= 0 ?
The solution to x^2-30x+150<= 0 is -5sqrt(3)+15<= x<= 5sqrt(3)+15