Solve 5x^2 37x -15

Question

Simplify the expression

185 x^{3} - 15

Evaluate

5 x^{2} \times 37 x - 15

Solution

More Steps

Evaluate

5 x^{2} \times 37 x

Multiply the terms

185 x^{2} \times x

Multiply the terms with the same base by adding their exponents

185 x^{2 + 1}

Add the numbers

185 x^{3}

185 x^{3} - 15

Show Solution

Factor the expression

5 (37 x^{3} - 3)

Evaluate

5 x^{2} \times 37 x - 15

Multiply

More Steps

Evaluate

5 x^{2} \times 37 x

Multiply the terms

185 x^{2} \times x

Multiply the terms with the same base by adding their exponents

185 x^{2 + 1}

Add the numbers

185 x^{3}

185 x^{3} - 15

Solution

5 (37 x^{3} - 3)

Show Solution

Find the roots

x = \frac{3 4107}{37}

Alternative Form

x \approx 0.432819

Evaluate

5 x^{2} \times 37 x - 15

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

5 x^{2} \times 37 x - 15 = 0

Multiply

More Steps

Multiply the terms

5 x^{2} \times 37 x

Multiply the terms

185 x^{2} \times x

Multiply the terms with the same base by adding their exponents

185 x^{2 + 1}

Add the numbers

185 x^{3}

185 x^{3} - 15 = 0

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

185 x^{3} = 0 + 15

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

185 x^{3} = 15

Divide both sides

\frac{185 x ^{3}}{185} = \frac{15}{185}

Divide the numbers

x^{3} = \frac{15}{185}

Cancel out the common factor 5

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

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

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

Calculate

x = 3 \frac{3}{37}

Solution

More Steps

Evaluate

3 \frac{3}{37}

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

\frac{3 3}{3 37}

Multiply by the Conjugate

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

Simplify

\frac{3 3 \times 3 1369}{3 37 \times 3 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 31369

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

3 3 \times 1369

Calculate the product

34107

\frac{3 4107}{3 37 \times 3 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

337 \times 3 3 7^{2}

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

3 37 \times 3 7^{2}

Calculate the product

3 3 7^{3}

Reduce the index of the radical and exponent with 3

37

\frac{3 4107}{37}

x = \frac{3 4107}{37}

Alternative Form

x \approx 0.432819

Show Solution