Solve 2x^3x-9 - Socratic AI (ScanMath)

Pergunta

Simplify the expression

2 x^{4} - 9

Evaluate

2 x^{3} \times x - 9

Solução

Mais Passos

Evaluate

2 x^{3} \times x

Multiply the terms with the same base by adding their exponents

2 x^{3 + 1}

Add the numbers

2 x^{4}

2 x^{4} - 9

Mostrar solução

x_{1} = - \frac{4 72}{2}, x_{2} = \frac{4 72}{2}

Alternative Form

x_{1} \approx - 1.456475, x_{2} \approx 1.456475

Evaluate

2 x^{3} \times x - 9

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

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

Multiply

Mais Passos

Multiply the terms

2 x^{3} \times x

Multiply the terms with the same base by adding their exponents

2 x^{3 + 1}

Add the numbers

2 x^{4}

2 x^{4} - 9 = 0

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

2 x^{4} = 0 + 9

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

2 x^{4} = 9

Divide both sides

\frac{2 x ^{4}}{2} = \frac{9}{2}

Divide the numbers

x^{4} = \frac{9}{2}

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

x = \pm 4 \frac{9}{2}

Simplify the expression

Mais Passos

Evaluate

4 \frac{9}{2}

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

\frac{4 9}{4 2}

Simplify the radical expression

Mais Passos

Evaluate

49

Write the number in exponential form with the base of 3

4 3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{4 2}

Multiply by the Conjugate

\frac{3 \times 4 2 ^{3}}{4 2 \times 4 2 ^{3}}

Simplify

\frac{3 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

Mais Passos

Evaluate

3 \times 48

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

4 3^{2} \times 48

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

4 3^{2} \times 8

Calculate the product

472

\frac{4 72}{4 2 \times 4 2 ^{3}}

Multiply the numbers

Mais Passos

Evaluate

42 \times 4 2^{3}

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

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 72}{2}

x = \pm \frac{4 72}{2}

Separate the equation into 2 possible cases

x = \frac{4 72}{2} x = - \frac{4 72}{2}

Solução

x_{1} = - \frac{4 72}{2}, x_{2} = \frac{4 72}{2}

Alternative Form

x_{1} \approx - 1.456475, x_{2} \approx 1.456475

Mostrar solução