Solve X^2(-x^2-64) <=64(-x^2-64)

Question

Solve the inequality

Solve for x

Solve for X

X > 8, x \in R X < - 8, x \in R

Evaluate

X^{2} (- x^{2} - 64) \leq 64 (- x^{2} - 64)

Calculate

More Steps

- X^{2} x^{2} - 64 X^{2} = 64 (- x^{2} - 64)

Calculate

More Steps

- X^{2} x^{2} - 64 X^{2} = - 64 x^{2} - 4096

Move the expression to the left side

- X^{2} x^{2} - 64 X^{2} - (- 64 x^{2} - 4096) \leq 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- X^{2} x^{2} - 64 X^{2} + 64 x^{2} + 4096 \leq 0

Collect like terms by calculating the sum or difference of their coefficients

(- X^{2} + 64) x^{2} - 64 X^{2} + 4096 \leq 0

Move the constant to the right side

(- X^{2} + 64) x^{2} \leq 64 X^{2} - 4096

Divide both sides

\frac{( - X ^{2} + 64 ) x ^{2}}{- X ^{2} + 64} \leq \frac{64 X ^{2} - 4096}{- X ^{2} + 64}

Divide the numbers

x^{2} \leq \frac{64 X ^{2} - 4096}{- X ^{2} + 64}

Divide the numbers

More Steps

x^{2} \leq - 64

Rewrite the inequalities

{x^{2} \leq - 64 64 - X^{2} > 0 {x^{2} \geq - 64 64 - X^{2} < 0

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x

{x \in / R 64 - X^{2} > 0 {x^{2} \geq - 64 64 - X^{2} < 0

Calculate

More Steps

{x \in / R - 8 < X < 8 {x^{2} \geq - 64 64 - X^{2} < 0

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is true for any value of x

{x \in / R - 8 < X < 8 {x \in R 64 - X^{2} < 0

Calculate

More Steps

{x \in / R - 8 < X < 8 {x \in R X \in (- \infty, - 8) \cup (8, + \infty)

Calculate

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(X, x) \in / R^{2} {x \in R X \in (- \infty, - 8) \cup (8, + \infty)

Calculate

(X, x) \in / R^{2} {X > 8 x \in R {X < - 8 x \in R

Rearrange the terms

{X > 8 x \in R {X < - 8 x \in R

Solution

X > 8, x \in R X < - 8, x \in R

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