Solve x-3 root(2)(x) 1

Question

Simplify the expression

x - 3 x

Evaluate

x - 3 x \times 1

Solution

x - 3 x

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(x - 3) x

Evaluate

x - 3 x \times 1

Multiply the terms

x - 3 x

Rewrite the expression

x \times x - 3 x

Solution

(x - 3) x

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x_{1} = 0, x_{2} = 9

Evaluate

x - 3 x \times 1

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

x - 3 x \times 1 = 0

Find the domain

x - 3 x \times 1 = 0, x \geq 0

Calculate

x - 3 x \times 1 = 0

Multiply the terms

x - 3 x = 0

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

- 3 x = - x

Divide both sides of the equation by - 1

3 x = x

Rewrite the expression

x = \frac{x}{3}

Evaluate

x = \frac{x}{3}, \frac{x}{3} \geq 0

Evaluate

x = \frac{x}{3}, x \geq 0

Solve the equation for x

More Steps

Evaluate

x = \frac{x}{3}

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

(x)^{2} = (\frac{x}{3})^{2}

Evaluate the power

x = \frac{x ^{2}}{9}

Cross multiply

x \times 9 = x^{2}

Simplify the equation

9 x = x^{2}

Move the expression to the left side

9 x - x^{2} = 0

Factor the expression

More Steps

Evaluate

9 x - x^{2}

Rewrite the expression

x \times 9 - x \times x

Factor out x from the expression

x (9 - x)

x (9 - x) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 9 - x = 0

Solve the equation for x

More Steps

Evaluate

9 - x = 0

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

- x = 0 - 9

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

- x = - 9

Change the signs on both sides of the equation

x = 9

x = 0 x = 9

x = 0 x = 9, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = 9

Solution

x_{1} = 0, x_{2} = 9

Show Solution