Solve -x^2 4x-7=0

Question

Solve the equation

x = - \frac{3 14}{2}

Alternative Form

x \approx - 1.205071

Evaluate

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

Multiply

More Steps

Evaluate

- x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 4

Add the numbers

- x^{3} \times 4

Use the commutative property to reorder the terms

- 4 x^{3}

- 4 x^{3} - 7 = 0

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

- 4 x^{3} = 0 + 7

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

- 4 x^{3} = 7

Change the signs on both sides of the equation

4 x^{3} = - 7

Divide both sides

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

Divide the numbers

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

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

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

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

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

Calculate

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

Solution

More Steps

Evaluate

3 - \frac{7}{4}

An odd root of a negative radicand is always a negative

- 3 \frac{7}{4}

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

- \frac{3 7}{3 4}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

- 37 \times 232

Multiply the terms

- 314 \times 2

Use the commutative property to reorder the terms

- 2314

\frac{- 2 3 14}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{- 2 3 14}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{- 2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{- 1}{2 ^{2 - 1}}

Subtract the terms

\frac{- 1}{2 ^{1}}

Simplify

\frac{- 1}{2}

\frac{- 3 14}{2}

Calculate

- \frac{3 14}{2}

x = - \frac{3 14}{2}

Alternative Form

x \approx - 1.205071

Show Solution