Solve x^39x-26 - ScanMath

Question

Simplify the expression

9 x^{4} - 26

Evaluate

x^{3} \times 9 x - 26

Solution

More Steps

Evaluate

x^{3} \times 9 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 9

Add the numbers

x^{4} \times 9

Use the commutative property to reorder the terms

9 x^{4}

9 x^{4} - 26

Show Solution

x_{1} = - \frac{4 234}{3}, x_{2} = \frac{4 234}{3}

Alternative Form

x_{1} \approx - 1.303715, x_{2} \approx 1.303715

Evaluate

x^{3} \times 9 x - 26

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

x^{3} \times 9 x - 26 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 9 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 9

Add the numbers

x^{4} \times 9

Use the commutative property to reorder the terms

9 x^{4}

9 x^{4} - 26 = 0

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

9 x^{4} = 0 + 26

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

9 x^{4} = 26

Divide both sides

\frac{9 x ^{4}}{9} = \frac{26}{9}

Divide the numbers

x^{4} = \frac{26}{9}

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

x = \pm 4 \frac{26}{9}

Simplify the expression

More Steps

Evaluate

4 \frac{26}{9}

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

\frac{4 26}{4 9}

Simplify the radical expression

More Steps

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{4 26}{3}

Multiply by the Conjugate

\frac{4 26 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

426 \times 3

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

426 \times 4 3^{2}

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

4 26 \times 3^{2}

Calculate the product

4234

\frac{4 234}{3 \times 3}

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

\frac{4 234}{3}

x = \pm \frac{4 234}{3}

Separate the equation into 2 possible cases

x = \frac{4 234}{3} x = - \frac{4 234}{3}

Solution

x_{1} = - \frac{4 234}{3}, x_{2} = \frac{4 234}{3}

Alternative Form

x_{1} \approx - 1.303715, x_{2} \approx 1.303715

Show Solution