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Popular >

2x^2-8x+5>= 0

Solution

2 x^{2} - 8 x + 5 \geq 0

Solution

x \leq - \frac{3}{2} + 2 or x \geq \frac{3}{2} + 2

+2

Interval Notation

(- \infty, - \frac{3}{2} + 2] \cup [\frac{3}{2} + 2, \infty)

Decimal Notation

x \leq 0.77525 \dots or x \geq 3.22474 \dots

Solution steps

2 x^{2} - 8 x + 5 \geq 0

Complete the square

2 x^{2} - 8 x + 5 : 2 (x - 2)^{2} - 3

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

Move

3

to the right side

2 (x - 2)^{2} \geq 3

Divide both sides by

2

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

For

u^{n} \geq a

, if

n

is even then

x - 2 \leq - \frac{3}{2} or x - 2 \geq \frac{3}{2}

x - 2 \leq - \frac{3}{2} : x \leq - \frac{3}{2} + 2

x - 2 \geq \frac{3}{2} : x \geq \frac{3}{2} + 2

Combine the intervals

x \leq - \frac{3}{2} + 2 or x \geq \frac{3}{2} + 2

Popular Examples

factor 81x^2+108x+36 factor

81 x^{2} + 108 x + 36

1 < 3 x + 4 < 16

\frac{x}{4} = 1

x^{3} + 4 x^{2} > 0

factor x^4+216x factor

x^{4} + 216 x

Frequently Asked Questions (FAQ)

What is 2x^2-8x+5>= 0 ?
The solution to 2x^2-8x+5>= 0 is x<=-sqrt(3/2)+2\lor x>= sqrt(3/2)+2