Solve x^2-64<=0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

- 8 \leq x \leq 8

Alternative Form

x \in [- 8, 8]

Evaluate

x^{2} - 64 \leq 0

Rewrite the expression

x^{2} - 64 = 0

Move the constant to the right-hand side and change its sign

x^{2} = 0 + 64

Removing 0 doesn't change the value,so remove it from the expression

x^{2} = 64

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 64

Simplify the expression

More Steps

x = \pm 8

Separate the equation into 2 possible cases

x = 8 x = - 8

Determine the test intervals using the critical values

x < - 8 - 8 < x < 8 x > 8

Choose a value form each interval

x_{1} = - 9 x_{2} = 0 x_{3} = 9

To determine if x < - 8 is the solution to the inequality,test if the chosen value x = - 9 satisfies the initial inequality

More Steps

x < - 8 is not a solution x_{2} = 0 x_{3} = 9

To determine if - 8 < x < 8 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 8 is not a solution - 8 < x < 8 is the solution x_{3} = 9

To determine if x > 8 is the solution to the inequality,test if the chosen value x = 9 satisfies the initial inequality

More Steps

x < - 8 is not a solution - 8 < x < 8 is the solution x > 8 is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

- 8 \leq x \leq 8 is the solution

Solution

- 8 \leq x \leq 8

Alternative Form

x \in [- 8, 8]

Show Solution