Solve sqrt(25-x^(2))

Question

Find the roots

x_{1} = - 5, x_{2} = 5

Evaluate

25 - x^{2}

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

25 - x^{2} = 0

Find the domain

More Steps

Evaluate

25 - x^{2} \geq 0

Rewrite the expression

- x^{2} \geq - 25

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

x^{2} \leq 25

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

x^{2} \leq 25

Calculate

∣ x ∣ \leq 5

Separate the inequality into 2 possible cases

{x \leq 5 x \geq - 5

Find the intersection

- 5 \leq x \leq 5

25 - x^{2} = 0, - 5 \leq x \leq 5

Calculate

25 - x^{2} = 0

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

25 - x^{2} = 0

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

- x^{2} = 0 - 25

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

- x^{2} = - 25

Change the signs on both sides of the equation

x^{2} = 25

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

x = \pm 25

Simplify the expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

x = \pm 5

Separate the equation into 2 possible cases

x = 5 x = - 5

Check if the solution is in the defined range

x = 5 x = - 5, - 5 \leq x \leq 5

Find the intersection of the solution and the defined range

x = 5 x = - 5

Solution

x_{1} = - 5, x_{2} = 5

Show Solution