What is -2x^2-5x+42<= 0 ?

The solution to -2x^2-5x+42 = 7/2

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-2x^2-5x+42<= 0

- 2 x^{2} - 5 x + 42 \leq 0

x \leq - 6 or x \geq \frac{7}{2}

Interval Notation

(- \infty, - 6] \cup [\frac{7}{2}, \infty)

Decimal Notation

x \leq - 6 or x \geq 3.5

Solution steps

- 2 x^{2} - 5 x + 42 \leq 0

Factor

- 2 x^{2} - 5 x + 42 : - (2 x - 7) (x + 6)

- (2 x - 7) (x + 6) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (2 x - 7) (x + 6)) (- 1) \geq 0 \cdot (- 1)

Simplify

(2 x - 7) (x + 6) \geq 0

Identify the intervals

x \leq - 6 or x \geq \frac{7}{2}

- 4 (x + 5) = - 4 x - 20

x - 4 = 17

2 t^{2} - 7 t + 6

y^{2} = - 64