What is (x+5)*(x-4)<= 6 ?

The solution to (x+5)*(x-4)<= 6 is (-sqrt(105)-1)/2 <= x<= (sqrt(105)-1)/2

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(x+5)*(x-4)<= 6

(x + 5) \cdot (x - 4) \leq 6

\frac{- 105 - 1}{2} \leq x \leq \frac{105 - 1}{2}

Solution steps

(x + 5) (x - 4) \leq 6

Rewrite in standard form

x^{2} + x - 26 \leq 0

Complete the square

x^{2} + x - 26 : (x + \frac{1}{2})^{2} - \frac{105}{4}

(x + \frac{1}{2})^{2} - \frac{105}{4} \leq 0

Move

\frac{105}{4}

to the right side

(x + \frac{1}{2})^{2} \leq \frac{105}{4}

For

u^{n} \leq a

, if

n

is even then

- \frac{105}{4} \leq x + \frac{1}{2} \leq \frac{105}{4}

a \leq u \leq b

then

a \leq u and u \leq b

- \frac{105}{4} \leq x + \frac{1}{2} and x + \frac{1}{2} \leq \frac{105}{4}

- \frac{105}{4} \leq x + \frac{1}{2} : x \geq \frac{- 105 - 1}{2}

x + \frac{1}{2} \leq \frac{105}{4} : x \leq \frac{105 - 1}{2}

Combine the intervals

x \geq \frac{- 105 - 1}{2} and x \leq \frac{105 - 1}{2}

Merge Overlapping Intervals

\frac{- 105 - 1}{2} \leq x \leq \frac{105 - 1}{2}

a^{2} + 14 a + 45

5 - 4 x \geq 3 x - 9

11 x^{2} + 100 x - 100

34 3^{- \frac{1}{3}}

(- 81)^{- \frac{1}{2}}

What is (x+5)*(x-4)<= 6 ?
The solution to (x+5)*(x-4)<= 6 is (-sqrt(105)-1)/2 <= x<= (sqrt(105)-1)/2