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Popular >

sqrt(0.5x^2)+1<= 4|x|

Solution

0.5 x^{2} + 1 \leq 4 ∣ x ∣

Solution

x \leq - 0.30368 \dots or x \geq 0.30368 \dots

+1

Interval Notation

(- \infty, - 0.30368 \dots] \cup [0.30368 \dots, \infty)

Solution steps

0.5 x^{2} + 1 \leq 4 ∣ x ∣

Subtract

1

from both sides

0.5 x^{2} + 1 - 1 \leq 4 ∣ x ∣ - 1

Simplify

0.5 x^{2} \leq 4 ∣ x ∣ - 1

If

f (x) \leq g (x)

then

g (x) \geq 0

4 ∣ x ∣ - 1 \geq 0 : x \leq - \frac{1}{4} or x \geq \frac{1}{4}

0.5 x^{2} \leq 4 ∣ x ∣ - 1 : x \leq - 0.30368 \dots or - 0.21244 \dots \leq x \leq 0.21244 \dots or x \geq 0.30368 \dots

Verify Solutions:

x \leq - 0.30368 \dots

True

, x \geq 0.30368 \dots

True

The solution is

x \leq - 0.30368 \dots or x \geq 0.30368 \dots

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2 x \cdot x^{3}

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2 x^{2} + x - 1

10 - \frac{b}{2} = 3

x^{2} - 10 x = - 25

simplify (3-sqrt(3))/(3+sqrt(3))simplify

\frac{3 - 3}{3 + 3}

Frequently Asked Questions (FAQ)

What is sqrt(0.5x^2)+1<= 4|x| ?
The solution to sqrt(0.5x^2)+1<= 4|x| is x<=-0.30368…\lor x>= 0.30368…