Solve x^2-3root5x 10

Question

Simplify the expression

x^{2} - 15 2 x

Evaluate

x^{2} - 3 5 x \times 10

Multiply the terms

x^{2} - 3 50 x

Simplify the root

More Steps

Evaluate

50 x

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 2 x

Write the number in exponential form with the base of 5

5^{2} \times 2 x

The root of a product is equal to the product of the roots of each factor

5^{2} \times 2 x

Reduce the index of the radical and exponent with 2

5 2 x

x^{2} - 3 \times 5 2 x

Solution

x^{2} - 15 2 x

Show Solution

Factor the expression

x \times (x x - 152)

Evaluate

x^{2} - 3 5 x \times 10

Multiply the terms

x^{2} - 3 50 x

Simplify the root

More Steps

Evaluate

50 x

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 2 x

Write the number in exponential form with the base of 5

5^{2} \times 2 x

The root of a product is equal to the product of the roots of each factor

5^{2} \times 2 x

Reduce the index of the radical and exponent with 2

5 2 x

x^{2} - 3 \times 5 2 x

Calculate

x^{2} - 15 2 x

Rewrite the expression

x \times x x - x \times 152

Solution

x \times (x x - 152)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 3450

Alternative Form

x_{1} = 0, x_{2} \approx 7.663094

Evaluate

x^{2} - 3 5 x \times 10

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

x^{2} - 3 5 x \times 10 = 0

Find the domain

More Steps

Evaluate

5 x \times 10 \geq 0

Multiply the terms

50 x \geq 0

Rewrite the expression

x \geq 0

x^{2} - 3 5 x \times 10 = 0, x \geq 0

Calculate

x^{2} - 3 5 x \times 10 = 0

Multiply the terms

x^{2} - 3 50 x = 0

Simplify the root

More Steps

Evaluate

50 x

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 2 x

Write the number in exponential form with the base of 5

5^{2} \times 2 x

The root of a product is equal to the product of the roots of each factor

5^{2} \times 2 x

Reduce the index of the radical and exponent with 2

5 2 x

x^{2} - 3 \times 5 2 x = 0

Multiply the terms

x^{2} - 15 2 x = 0

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

- 15 2 x = - x^{2}

Divide both sides of the equation by - 1

15 2 x = x^{2}

Rewrite the expression

2 x = \frac{x ^{2}}{15}

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

(2 x)^{2} = (\frac{x ^{2}}{15})^{2}

Evaluate the power

2 x = \frac{x ^{4}}{225}

Cross multiply

2 x \times 225 = x^{4}

Simplify the equation

450 x = x^{4}

Move the expression to the left side

450 x - x^{4} = 0

Factor the expression

x (450 - x^{3}) = 0

Separate the equation into 2 possible cases

x = 0 450 - x^{3} = 0

Solve the equation

More Steps

Evaluate

450 - x^{3} = 0

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

- x^{3} = 0 - 450

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

- x^{3} = - 450

Change the signs on both sides of the equation

x^{3} = 450

Take the 3 -th root on both sides of the equation

3 x^{3} = 3450

Calculate

x = 3450

x = 0 x = 3450

Check if the solution is in the defined range

x = 0 x = 3450, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = 3450

Solution

x_{1} = 0, x_{2} = 3450

Alternative Form

x_{1} = 0, x_{2} \approx 7.663094

Show Solution