What is (2x-1)(x+3)<= x(3x-9) ?

The solution to (2x-1)(x+3) = sqrt(46)+7

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(2x-1)(x+3)<= x(3x-9)

(2 x - 1) (x + 3) \leq x (3 x - 9)

x \leq - 46 + 7 or x \geq 46 + 7

Interval Notation

(- \infty, - 46 + 7] \cup [46 + 7, \infty)

Decimal Notation

x \leq 0.21767 \dots or x \geq 13.78232 \dots

Solution steps

(2 x - 1) (x + 3) \leq x (3 x - 9)

Rewrite in standard form

- x^{2} + 14 x - 3 \leq 0

Complete the square

- x^{2} + 14 x - 3 : - (x - 7)^{2} + 46

- (x - 7)^{2} + 46 \leq 0

Move

46

to the right side

- (x - 7)^{2} \leq - 46

Multiply both sides by

- 1

(x - 7)^{2} \geq 46

For

u^{n} \geq a

, if

n

is even then

x - 7 \leq - 46 or x - 7 \geq 46

x - 7 \leq - 46 : x \leq - 46 + 7

x - 7 \geq 46 : x \geq 46 + 7

Combine the intervals

x \leq - 46 + 7 or x \geq 46 + 7

x - 9 = 4

2 x + 12

x^{2} - 7 x + 12

- \frac{16}{4}

2 \cdot 10

What is (2x-1)(x+3)<= x(3x-9) ?
The solution to (2x-1)(x+3)<= x(3x-9) is x<=-sqrt(46)+7\lor x>= sqrt(46)+7