What is x(x+7.5)>38.5 ?

The solution to x(x+7.5)>38.5 is x sqrt(52.5625)-3.75

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x(x+7.5)>38.5

x (x + 7.5) > 38.5

x < - 52.5625 - 3.75 or x > 52.5625 - 3.75

Interval Notation

(- \infty, - 52.5625 - 3.75) \cup (52.5625 - 3.75, \infty)

Decimal Notation

x < - 11 or x > 3.5

Solution steps

x (x + 7.5) > 38.5

Rewrite in standard form

x^{2} + 7.5 x - 38.5 > 0

Complete the square

x^{2} + 7.5 x - 38.5 : (x + 3.75)^{2} - 52.5625

(x + 3.75)^{2} - 52.5625 > 0

Move

52.5625

to the right side

(x + 3.75)^{2} > 52.5625

For

u^{n} > a

, if

n

is even then

x + 3.75 < - 52.5625 or x + 3.75 > 52.5625

x + 3.75 < - 52.5625 : x < - 52.5625 - 3.75

x + 3.75 > 52.5625 : x > 52.5625 - 3.75

Combine the intervals

x < - 52.5625 - 3.75 or x > 52.5625 - 3.75

- \frac{7}{15} x + 26 = \frac{1}{3} x + 2

7 x - 3 (x + 2) = x + 5

(\frac{1}{4} + \frac{6}{15}) \div (\frac{2}{9} - \frac{3}{7})

\frac{1}{3} + \frac{1}{2}

145 \cdot \frac{π}{180}

What is x(x+7.5)>38.5 ?
The solution to x(x+7.5)>38.5 is x<-sqrt(52.5625)-3.75\lor x>sqrt(52.5625)-3.75