Solve 2x^2 x-53 - ScanMath

Question

Simplify the expression

2 x^{3} - 53

Evaluate

2 x^{2} \times x - 53

Solution

More Steps

Evaluate

2 x^{2} \times x

Multiply the terms with the same base by adding their exponents

2 x^{2 + 1}

Add the numbers

2 x^{3}

2 x^{3} - 53

Show Solution

x = \frac{3 212}{2}

Alternative Form

x \approx 2.981366

Evaluate

2 x^{2} \times x - 53

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

2 x^{2} \times x - 53 = 0

Multiply

More Steps

Multiply the terms

2 x^{2} \times x

Multiply the terms with the same base by adding their exponents

2 x^{2 + 1}

Add the numbers

2 x^{3}

2 x^{3} - 53 = 0

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

2 x^{3} = 0 + 53

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

2 x^{3} = 53

Divide both sides

\frac{2 x ^{3}}{2} = \frac{53}{2}

Divide the numbers

x^{3} = \frac{53}{2}

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

3 x^{3} = 3 \frac{53}{2}

Calculate

x = 3 \frac{53}{2}

Solution

More Steps

Evaluate

3 \frac{53}{2}

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

\frac{3 53}{3 2}

Multiply by the Conjugate

\frac{3 53 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 53 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

353 \times 34

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

3 53 \times 4

Calculate the product

3212

\frac{3 212}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 212}{2}

x = \frac{3 212}{2}

Alternative Form

x \approx 2.981366

Show Solution