Solve x^22root3-9

Question

Simplify the expression

Solution

23 \times x^{2} - 9

Evaluate

x^{2} \times 23 - 9

Solution

More Steps

Evaluate

x^{2} \times 23

Use the commutative property to reorder the terms

2 x^{2} 3

Calculate the product

23 \times x^{2}

23 \times x^{2} - 9

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = - \frac{4 108}{2}, x_{2} = \frac{4 108}{2}

Alternative Form

x_{1} \approx - 1.611855, x_{2} \approx 1.611855

Evaluate

x^{2} \times 23 - 9

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

x^{2} \times 23 - 9 = 0

Multiply the terms

More Steps

Multiply the terms

x^{2} \times 23

Use the commutative property to reorder the terms

2 x^{2} 3

Calculate the product

23 \times x^{2}

23 \times x^{2} - 9 = 0

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

23 \times x^{2} = 0 + 9

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

23 \times x^{2} = 9

Divide both sides

\frac{2 3 \times x ^{2}}{2 3} = \frac{9}{2 3}

Divide the numbers

x^{2} = \frac{9}{2 3}

Calculate

More Steps

Evaluate

\frac{9}{2 3}

Multiply by the Conjugate

\frac{9 3}{2 3 \times 3}

Calculate

\frac{9 3}{2 \times 3}

Simplify

\frac{9 3}{6}

Reduce the fraction

\frac{3 3}{2}

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

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

x = \pm \frac{3 3}{2}

Simplify the expression

More Steps

Evaluate

\frac{3 3}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 3}{2}

Simplify the radical expression

More Steps

Evaluate

33

Rewrite the expression

3 \times 3

Simplify the root

427

\frac{4 27}{2}

Multiply by the Conjugate

\frac{4 27 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

427 \times 2

Use n a = mn a^{m} to expand the expression

427 \times 4 2^{2}

The product of roots with the same index is equal to the root of the product

4 27 \times 2^{2}

Calculate the product

4108

\frac{4 108}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 108}{2}

x = \pm \frac{4 108}{2}

Separate the equation into 2 possible cases

x = \frac{4 108}{2} x = - \frac{4 108}{2}

Solution

x_{1} = - \frac{4 108}{2}, x_{2} = \frac{4 108}{2}

Alternative Form

x_{1} \approx - 1.611855, x_{2} \approx 1.611855

Show Solution

X^22root3 9

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression