Solve (x^2 3x-5)^2

Question

Simplify the expression

9 x^{6} - 30 x^{3} + 25

Evaluate

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

Multiply

More Steps

Evaluate

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

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

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

(3 x^{3})^{2} - 2 \times 3 x^{3} \times 5 + 5^{2}

Solution

9 x^{6} - 30 x^{3} + 25

Show Solution

x = \frac{3 45}{3}

Alternative Form

x \approx 1.185631

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

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

The only way a power can be 0 is when the base equals 0

3 x^{3} - 5 = 0

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

3 x^{3} = 0 + 5

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

3 x^{3} = 5

Divide both sides

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

Divide the numbers

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

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

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

Calculate

x = 3 \frac{5}{3}

Solution

More Steps

Evaluate

3 \frac{5}{3}

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

\frac{3 5}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{3 5 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 39

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

3 5 \times 9

Calculate the product

345

\frac{3 45}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 45}{3}

x = \frac{3 45}{3}

Alternative Form

x \approx 1.185631

Show Solution