Solve 49-14x x^2 - ScanMath

Question

Simplify the expression

49 - 14 x^{3}

Evaluate

49 - 14 x \times x^{2}

Solution

More Steps

Evaluate

14 x \times x^{2}

Multiply the terms with the same base by adding their exponents

14 x^{1 + 2}

Add the numbers

14 x^{3}

49 - 14 x^{3}

Show Solution

Factor the expression

7 (7 - 2 x^{3})

Evaluate

49 - 14 x \times x^{2}

Multiply

More Steps

Evaluate

14 x \times x^{2}

Multiply the terms with the same base by adding their exponents

14 x^{1 + 2}

Add the numbers

14 x^{3}

49 - 14 x^{3}

Solution

7 (7 - 2 x^{3})

Show Solution

Find the roots

x = \frac{3 28}{2}

Alternative Form

x \approx 1.518294

Evaluate

49 - 14 x \times x^{2}

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

49 - 14 x \times x^{2} = 0

Multiply

More Steps

Multiply the terms

14 x \times x^{2}

Multiply the terms with the same base by adding their exponents

14 x^{1 + 2}

Add the numbers

14 x^{3}

49 - 14 x^{3} = 0

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

- 14 x^{3} = 0 - 49

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

- 14 x^{3} = - 49

Change the signs on both sides of the equation

14 x^{3} = 49

Divide both sides

\frac{14 x ^{3}}{14} = \frac{49}{14}

Divide the numbers

x^{3} = \frac{49}{14}

Cancel out the common factor 7

x^{3} = \frac{7}{2}

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

3 x^{3} = 3 \frac{7}{2}

Calculate

x = 3 \frac{7}{2}

Solution

More Steps

Evaluate

3 \frac{7}{2}

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

\frac{3 7}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 7 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 34

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

3 7 \times 4

Calculate the product

328

\frac{3 28}{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 28}{2}

x = \frac{3 28}{2}

Alternative Form

x \approx 1.518294

Show Solution