What is 4x^2-100x-1000>= 0 ?

The solution to 4x^2-100x-1000>= 0 is x = (5sqrt(65)+25)/2

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4x^2-100x-1000>= 0

4 x^{2} - 100 x - 1000 \geq 0

x \leq \frac{- 5 65 + 25}{2} or x \geq \frac{5 65 + 25}{2}

Interval Notation

(- \infty, \frac{- 5 65 + 25}{2}] \cup [\frac{5 65 + 25}{2}, \infty)

Decimal Notation

x \leq - 7.65564 \dots or x \geq 32.65564 \dots

Solution steps

4 x^{2} - 100 x - 1000 \geq 0

Rewrite in standard form

x^{2} - 25 x - 250 \geq 0

Complete the square

x^{2} - 25 x - 250 : (x - \frac{25}{2})^{2} - \frac{1625}{4}

(x - \frac{25}{2})^{2} - \frac{1625}{4} \geq 0

Move

\frac{1625}{4}

to the right side

(x - \frac{25}{2})^{2} \geq \frac{1625}{4}

For

u^{n} \geq a

, if

n

is even then

x - \frac{25}{2} \leq - \frac{1625}{4} or x - \frac{25}{2} \geq \frac{1625}{4}

x - \frac{25}{2} \leq - \frac{1625}{4} : x \leq \frac{- 5 65 + 25}{2}

x - \frac{25}{2} \geq \frac{1625}{4} : x \geq \frac{5 65 + 25}{2}

Combine the intervals

x \leq \frac{- 5 65 + 25}{2} or x \geq \frac{5 65 + 25}{2}

4 y^{2} - 11 y + 6

3 (2 X - 3) + 2 (2 X - 2) + 10 = 5 X + 17

4 x + 5 > 49

- 2 w^{2} - w + 21

6 (- \frac{3}{2})

What is 4x^2-100x-1000>= 0 ?
The solution to 4x^2-100x-1000>= 0 is x<= (-5sqrt(65)+25)/2 \lor x>= (5sqrt(65)+25)/2