Solve sqrt(9-x^2)

Question

Find the roots

x_{1} = - 3, x_{2} = 3

Evaluate

9 - x^{2}

To find the roots of the expression,set the expression equal to 0

9 - x^{2} = 0

Find the domain

More Steps

Evaluate

9 - x^{2} \geq 0

Rewrite the expression

- x^{2} \geq - 9

Change the signs on both sides of the inequality and flip the inequality sign

x^{2} \leq 9

Take the 2 -th root on both sides of the inequality

x^{2} \leq 9

Calculate

∣ x ∣ \leq 3

Separate the inequality into 2 possible cases

{x \leq 3 x \geq - 3

Find the intersection

- 3 \leq x \leq 3

9 - x^{2} = 0, - 3 \leq x \leq 3

Calculate

9 - x^{2} = 0

The only way a root could be 0 is when the radicand equals 0

9 - x^{2} = 0

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

- x^{2} = 0 - 9

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

- x^{2} = - 9

Change the signs on both sides of the equation

x^{2} = 9

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

x = \pm 9

Simplify the expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

x = \pm 3

Separate the equation into 2 possible cases

x = 3 x = - 3

Check if the solution is in the defined range

x = 3 x = - 3, - 3 \leq x \leq 3

Find the intersection of the solution and the defined range

x = 3 x = - 3

Solution

x_{1} = - 3, x_{2} = 3

Show Solution