What is 15-2x>= x^2 ?

The solution to 15-2x>= x^2 is -5<= x<= 3

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15-2x>= x^2

15 - 2 x \geq x^{2}

- 5 \leq x \leq 3

Interval Notation

[- 5, 3]

Solution steps

15 - 2 x \geq x^{2}

Rewrite in standard form

15 - 2 x - x^{2} \geq 0

Factor

15 - 2 x - x^{2} : - (x - 3) (x + 5)

- (x - 3) (x + 5) \geq 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 3) (x + 5)) (- 1) \leq 0 \cdot (- 1)

Simplify

(x - 3) (x + 5) \leq 0

Identify the intervals

- 5 \leq x \leq 3

\frac{5}{2} x + 7 = x + \frac{11}{2}

3 x = 48

\frac{x + 7}{x - 7} < 0

x^{2} + (0 - 8)^{2} = 64

\frac{5}{6} + \frac{4}{3}