Solve -4x^216x-7 - Socratic AI (ScanMath)

Question

Simplify the expression

- 64 x^{3} - 7

Evaluate

- 4 x^{2} \times 16 x - 7

Solution

More Steps

Evaluate

- 4 x^{2} \times 16 x

Multiply the terms

- 64 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 64 x^{2 + 1}

Add the numbers

- 64 x^{3}

- 64 x^{3} - 7

Show Solution

x = - \frac{3 7}{4}

Alternative Form

x \approx - 0.478233

Evaluate

- 4 x^{2} \times 16 x - 7

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

- 4 x^{2} \times 16 x - 7 = 0

Multiply

More Steps

Multiply the terms

- 4 x^{2} \times 16 x

Multiply the terms

- 64 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 64 x^{2 + 1}

Add the numbers

- 64 x^{3}

- 64 x^{3} - 7 = 0

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

- 64 x^{3} = 0 + 7

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

- 64 x^{3} = 7

Change the signs on both sides of the equation

64 x^{3} = - 7

Divide both sides

\frac{64 x ^{3}}{64} = \frac{- 7}{64}

Divide the numbers

x^{3} = \frac{- 7}{64}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{7}{64}

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

3 x^{3} = 3 - \frac{7}{64}

Calculate

x = 3 - \frac{7}{64}

Solution

More Steps

Evaluate

3 - \frac{7}{64}

An odd root of a negative radicand is always a negative

- 3 \frac{7}{64}

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

- \frac{3 7}{3 64}

Simplify the radical expression

More Steps

Evaluate

364

Write the number in exponential form with the base of 4

3 4^{3}

Reduce the index of the radical and exponent with 3

4

- \frac{3 7}{4}

x = - \frac{3 7}{4}

Alternative Form

x \approx - 0.478233

Show Solution