Solve 4x^(2) 8x-21=0

Question

Solve the equation

x = \frac{3 42}{4}

Alternative Form

x \approx 0.869007

Evaluate

4 x^{2} \times 8 x - 21 = 0

Multiply

More Steps

Evaluate

4 x^{2} \times 8 x

Multiply the terms

32 x^{2} \times x

Multiply the terms with the same base by adding their exponents

32 x^{2 + 1}

Add the numbers

32 x^{3}

32 x^{3} - 21 = 0

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

32 x^{3} = 0 + 21

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

32 x^{3} = 21

Divide both sides

\frac{32 x ^{3}}{32} = \frac{21}{32}

Divide the numbers

x^{3} = \frac{21}{32}

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

3 x^{3} = 3 \frac{21}{32}

Calculate

x = 3 \frac{21}{32}

Simplify the root

More Steps

Evaluate

3 \frac{21}{32}

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

\frac{3 21}{3 32}

Simplify the radical expression

More Steps

Evaluate

332

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

3 8 \times 4

Write the number in exponential form with the base of 2

3 2^{3} \times 4

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

3 2^{3} \times 34

Reduce the index of the radical and exponent with 3

234

\frac{3 21}{2 3 4}

Multiply by the Conjugate

\frac{3 21 \times 3 4 ^{2}}{2 3 4 \times 3 4 ^{2}}

Simplify

\frac{3 21 \times 2 3 2}{2 3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 232

Multiply the terms

342 \times 2

Use the commutative property to reorder the terms

2342

\frac{2 3 42}{2 3 4 \times 3 4 ^{2}}

Multiply the numbers

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Evaluate

234 \times 3 4^{2}

Multiply the terms

2 \times 2^{2}

Calculate the product

2^{3}

\frac{2 3 42}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{3}}

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

\frac{1}{2 ^{3 - 1}}

Subtract the terms

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

\frac{3 42}{2 ^{2}}

x = \frac{3 42}{2 ^{2}}

Solution

x = \frac{3 42}{4}

Alternative Form

x \approx 0.869007

Show Solution