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Popular >

4x^2-56x+189>0

Solution

4 x^{2} - 56 x + 189 > 0

Solution

x < - \frac{7}{2} + 7 or x > \frac{7}{2} + 7

+2

Interval Notation

(- \infty, - \frac{7}{2} + 7) \cup (\frac{7}{2} + 7, \infty)

Decimal Notation

x < 5.67712 \dots or x > 8.32287 \dots

Solution steps

4 x^{2} - 56 x + 189 > 0

Complete the square

4 x^{2} - 56 x + 189 : 4 (x - 7)^{2} - 7

4 (x - 7)^{2} - 7 > 0

Move

7

to the right side

4 (x - 7)^{2} > 7

Divide both sides by

4

(x - 7)^{2} > \frac{7}{4}

For

u^{n} > a

, if

n

is even then

x - 7 < - \frac{7}{4} or x - 7 > \frac{7}{4}

x - 7 < - \frac{7}{4} : x < - \frac{7}{2} + 7

x - 7 > \frac{7}{4} : x > \frac{7}{2} + 7

Combine the intervals

x < - \frac{7}{2} + 7 or x > \frac{7}{2} + 7

Popular Examples

3 = - 4 x

simplify n/(n+3)+(12n)/(n-3)-9/(n^2-9)simplify

\frac{n}{n + 3} + \frac{12 n}{n - 3} - \frac{9}{n ^{2} - 9}

factor 3b^2-6b factor

3 b^{2} - 6 b

4(x^2+14x+49)-1=0

4 (x^{2} + 14 x + 49) - 1 = 0

simplify 5/19*6 simplify

\frac{5}{19} \cdot 6

Frequently Asked Questions (FAQ)

What is 4x^2-56x+189>0 ?
The solution to 4x^2-56x+189>0 is x<-(sqrt(7))/2+7\lor x>(sqrt(7))/2+7