Solve 7x^2 32x-100

Question

Simplify the expression

224 x^{3} - 100

Evaluate

7 x^{2} \times 32 x - 100

Solution

More Steps

Evaluate

7 x^{2} \times 32 x

Multiply the terms

224 x^{2} \times x

Multiply the terms with the same base by adding their exponents

224 x^{2 + 1}

Add the numbers

224 x^{3}

224 x^{3} - 100

Show Solution

Factor the expression

4 (56 x^{3} - 25)

Evaluate

7 x^{2} \times 32 x - 100

Multiply

More Steps

Evaluate

7 x^{2} \times 32 x

Multiply the terms

224 x^{2} \times x

Multiply the terms with the same base by adding their exponents

224 x^{2 + 1}

Add the numbers

224 x^{3}

224 x^{3} - 100

Solution

4 (56 x^{3} - 25)

Show Solution

Find the roots

x = \frac{3 1225}{14}

Alternative Form

x \approx 0.764277

Evaluate

7 x^{2} \times 32 x - 100

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

7 x^{2} \times 32 x - 100 = 0

Multiply

More Steps

Multiply the terms

7 x^{2} \times 32 x

Multiply the terms

224 x^{2} \times x

Multiply the terms with the same base by adding their exponents

224 x^{2 + 1}

Add the numbers

224 x^{3}

224 x^{3} - 100 = 0

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

224 x^{3} = 0 + 100

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

224 x^{3} = 100

Divide both sides

\frac{224 x ^{3}}{224} = \frac{100}{224}

Divide the numbers

x^{3} = \frac{100}{224}

Cancel out the common factor 4

x^{3} = \frac{25}{56}

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

3 x^{3} = 3 \frac{25}{56}

Calculate

x = 3 \frac{25}{56}

Solution

More Steps

Evaluate

3 \frac{25}{56}

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

\frac{3 25}{3 56}

Simplify the radical expression

More Steps

Evaluate

356

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 7

Write the number in exponential form with the base of 2

3 2^{3} \times 7

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 37

Reduce the index of the radical and exponent with 3

237

\frac{3 25}{2 3 7}

Multiply by the Conjugate

\frac{3 25 \times 3 7 ^{2}}{2 3 7 \times 3 7 ^{2}}

Simplify

\frac{3 25 \times 3 49}{2 3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

325 \times 349

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

3 25 \times 49

Calculate the product

31225

\frac{3 1225}{2 3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

237 \times 3 7^{2}

Multiply the terms

2 \times 7

Multiply the terms

14

\frac{3 1225}{14}

x = \frac{3 1225}{14}

Alternative Form

x \approx 0.764277

Show Solution