What is rr+5(-2r-10)<=-4r-1+6r ?

The solution to rr+5(-2r-10)<=-4r-1+6r is -sqrt(85)+6<= r<= sqrt(85)+6

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Solve the Inequality for r r+5(-2r-10)<=-4r-1+6r

rr + 5 (- 2 r - 10) \leq - 4 r - 1 + 6 r

- 85 + 6 \leq r \leq 85 + 6

Solution steps

rr + 5 (- 2 r - 10) \leq - 4 r - 1 + 6 r

Rewrite in standard form

r^{2} - 12 r - 49 \leq 0

Complete the square

r^{2} - 12 r - 49 : (r - 6)^{2} - 85

(r - 6)^{2} - 85 \leq 0

Move

85

to the right side

(r - 6)^{2} \leq 85

For

u^{n} \leq a

, if

n

is even then

- 85 \leq r - 6 \leq 85

a \leq u \leq b

then

a \leq u and u \leq b

- 85 \leq r - 6 and r - 6 \leq 85

- 85 \leq r - 6 : r \geq - 85 + 6

r - 6 \leq 85 : r \leq 85 + 6

Combine the intervals

r \geq - 85 + 6 and r \leq 85 + 6

Merge Overlapping Intervals

- 85 + 6 \leq r \leq 85 + 6

10.25%

11.5%

2 x^{2} - x - 4 = 0

x, 14 = - (x - 8)

- \frac{14}{35}

What is rr+5(-2r-10)<=-4r-1+6r ?
The solution to rr+5(-2r-10)<=-4r-1+6r is -sqrt(85)+6<= r<= sqrt(85)+6