Solve 2x^2 - 3^(1/2)x 9

Question

Simplify the expression

2 x^{2} - 93 \times x

Evaluate

2 x^{2} - 3^{\frac{1}{2}} x \times 9

Multiply

More Steps

Evaluate

3^{\frac{1}{2}} x \times 9

Transform the expression

3^{\frac{1}{2}} x \times 3^{2}

Multiply the terms with the same base by adding their exponents

3^{\frac{1}{2} + 2} x

Add the numbers

More Steps

Evaluate

\frac{1}{2} + 2

Reduce fractions to a common denominator

\frac{1}{2} + \frac{2 \times 2}{2}

Write all numerators above the common denominator

\frac{1 + 2 \times 2}{2}

Multiply the numbers

\frac{1 + 4}{2}

Add the numbers

\frac{5}{2}

3^{\frac{5}{2}} x

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

Solution

2 x^{2} - 93 \times x

Show Solution

Factor the expression

x (2 x - 93)

Evaluate

2 x^{2} - 3^{\frac{1}{2}} x \times 9

Multiply

More Steps

Evaluate

3^{\frac{1}{2}} x \times 9

Transform the expression

3^{\frac{1}{2}} x \times 3^{2}

Multiply the terms with the same base by adding their exponents

3^{\frac{1}{2} + 2} x

Add the numbers

More Steps

Evaluate

\frac{1}{2} + 2

Reduce fractions to a common denominator

\frac{1}{2} + \frac{2 \times 2}{2}

Write all numerators above the common denominator

\frac{1 + 2 \times 2}{2}

Multiply the numbers

\frac{1 + 4}{2}

Add the numbers

\frac{5}{2}

3^{\frac{5}{2}} x

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

Calculate

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

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out x from the expression

x (2 x - 3 \times 3^{2})

Solution

x (2 x - 93)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{9 3}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 7.794229

Evaluate

2 x^{2} - 3^{\frac{1}{2}} x \times 9

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

2 x^{2} - 3^{\frac{1}{2}} x \times 9 = 0

Multiply

More Steps

Multiply the terms

3^{\frac{1}{2}} x \times 9

Transform the expression

3^{\frac{1}{2}} x \times 3^{2}

Multiply the terms with the same base by adding their exponents

3^{\frac{1}{2} + 2} x

Add the numbers

More Steps

Evaluate

\frac{1}{2} + 2

Reduce fractions to a common denominator

\frac{1}{2} + \frac{2 \times 2}{2}

Write all numerators above the common denominator

\frac{1 + 2 \times 2}{2}

Multiply the numbers

\frac{1 + 4}{2}

Add the numbers

\frac{5}{2}

3^{\frac{5}{2}} x

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

Factor the expression

More Steps

Evaluate

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

Rewrite the expression

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

Factor out x from the expression

x (2 x - 3^{\frac{5}{2}})

x (2 x - 3^{\frac{5}{2}}) = 0

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

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

Solve the equation for x

More Steps

Evaluate

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

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

2 x = 0 + 3^{\frac{5}{2}}

Add the numbers

More Steps

Evaluate

0 + 3^{\frac{5}{2}}

Rewrite the expression

0 + 93

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

93

2 x = 93

Divide both sides

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

Divide the numbers

x = \frac{9 3}{2}

x = 0 x = \frac{9 3}{2}

Solution

x_{1} = 0, x_{2} = \frac{9 3}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 7.794229

Show Solution