What is (x-1)^2-(x+3)^2-x^2>7 ?

The solution to (x-1)^2-(x+3)^2-x^2>7 is -5<x<-3

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(x-1)^2-(x+3)^2-x^2>7

(x - 1)^{2} - (x + 3)^{2} - x^{2} > 7

- 5 < x < - 3

Interval Notation

(- 5, - 3)

Solution steps

(x - 1)^{2} - (x + 3)^{2} - x^{2} > 7

Rewrite in standard form

- x^{2} - 8 x - 15 > 0

Factor

- x^{2} - 8 x - 15 : - (x + 3) (x + 5)

- (x + 3) (x + 5) > 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

(x + 3) (x + 5) < 0

Identify the intervals

- 5 < x < - 3

r^{2} = 96

11 x + 9 = 6 x - 1

k^{2} - 28 k - 29

\frac{x - 5}{3 x + 7} \leq 4

3 x \geq - 15

What is (x-1)^2-(x+3)^2-x^2>7 ?
The solution to (x-1)^2-(x+3)^2-x^2>7 is -5<x<-3