What is -8x^4+6x^2+5<= 0 ?

The solution to -8x^4+6x^2+5 = (sqrt(5))/2

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-8x^4+6x^2+5<= 0

- 8 x^{4} + 6 x^{2} + 5 \leq 0

x \leq - \frac{5}{2} or x \geq \frac{5}{2}

Interval Notation

(- \infty, - \frac{5}{2}] \cup [\frac{5}{2}, \infty)

Decimal Notation

x \leq - 1.11803 \dots or x \geq 1.11803 \dots

Solution steps

- 8 x^{4} + 6 x^{2} + 5 \leq 0

Factor

- 8 x^{4} + 6 x^{2} + 5 : - (2 x^{2} + 1) (2 x + 5) (2 x - 5)

- (2 x^{2} + 1) (2 x + 5) (2 x - 5) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (2 x^{2} + 1) (2 x + 5) (2 x - 5)) (- 1) \geq 0 \cdot (- 1)

Simplify

(2 x^{2} + 1) (2 x + 5) (2 x - 5) \geq 0

Identify the intervals

x \leq - \frac{5}{2} or x \geq \frac{5}{2}

\frac{( ( x + 7 ) ^{2} )}{( ( 3 + x ) ( 2 - x ) )} \geq 0

\frac{4 ( x ^{2} + 2 )}{( x ^{2} - 1 )} < - 2

(x - 5)^{3} + 9 \geq 10

(x^{2} - 3 x + 2) (x^{2} - 3 x^{2}) (4 - x^{2}) \leq 0

\frac{( 3 x + 4 )}{( 2 x - 1 )} < 2

What is -8x^4+6x^2+5<= 0 ?
The solution to -8x^4+6x^2+5<= 0 is x<=-(sqrt(5))/2 \lor x>= (sqrt(5))/2