Solve 28x^37+73x^37-37

Question

Simplify the expression

707 x^{3} - 37

Evaluate

28 x^{3} \times 7 + 73 x^{3} \times 7 - 37

Multiply the terms

196 x^{3} + 73 x^{3} \times 7 - 37

Multiply the terms

196 x^{3} + 511 x^{3} - 37

Solution

More Steps

Evaluate

196 x^{3} + 511 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(196 + 511) x^{3}

Add the numbers

707 x^{3}

707 x^{3} - 37

Show Solution

x = \frac{3 37 \times 70 7 ^{2}}{707}

Alternative Form

x \approx 0.374048

Evaluate

28 x^{3} \times 7 + 73 x^{3} \times 7 - 37

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

28 x^{3} \times 7 + 73 x^{3} \times 7 - 37 = 0

Multiply the terms

196 x^{3} + 73 x^{3} \times 7 - 37 = 0

Multiply the terms

196 x^{3} + 511 x^{3} - 37 = 0

Add the terms

More Steps

Evaluate

196 x^{3} + 511 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(196 + 511) x^{3}

Add the numbers

707 x^{3}

707 x^{3} - 37 = 0

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

707 x^{3} = 0 + 37

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

707 x^{3} = 37

Divide both sides

\frac{707 x ^{3}}{707} = \frac{37}{707}

Divide the numbers

x^{3} = \frac{37}{707}

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

3 x^{3} = 3 \frac{37}{707}

Calculate

x = 3 \frac{37}{707}

Solution

More Steps

Evaluate

3 \frac{37}{707}

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

\frac{3 37}{3 707}

Multiply by the Conjugate

\frac{3 37 \times 3 70 7 ^{2}}{3 707 \times 3 70 7 ^{2}}

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

\frac{3 37 \times 70 7 ^{2}}{3 707 \times 3 70 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

3707 \times 3 70 7^{2}

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

3 707 \times 70 7^{2}

Calculate the product

3 70 7^{3}

Reduce the index of the radical and exponent with 3

707

\frac{3 37 \times 70 7 ^{2}}{707}

x = \frac{3 37 \times 70 7 ^{2}}{707}

Alternative Form

x \approx 0.374048

Show Solution