Solve 4x^212x-43=0

Question

Solve the equation

x = \frac{3 1548}{12}

Alternative Form

x \approx 0.963997

Evaluate

4 x^{2} \times 12 x - 43 = 0

Multiply

More Steps

Evaluate

4 x^{2} \times 12 x

Multiply the terms

48 x^{2} \times x

Multiply the terms with the same base by adding their exponents

48 x^{2 + 1}

Add the numbers

48 x^{3}

48 x^{3} - 43 = 0

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

48 x^{3} = 0 + 43

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

48 x^{3} = 43

Divide both sides

\frac{48 x ^{3}}{48} = \frac{43}{48}

Divide the numbers

x^{3} = \frac{43}{48}

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

3 x^{3} = 3 \frac{43}{48}

Calculate

x = 3 \frac{43}{48}

Solution

More Steps

Evaluate

3 \frac{43}{48}

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

\frac{3 43}{3 48}

Simplify the radical expression

More Steps

Evaluate

348

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

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

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

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

\frac{3 43}{2 3 6}

Multiply by the Conjugate

\frac{3 43 \times 3 6 ^{2}}{2 3 6 \times 3 6 ^{2}}

Simplify

\frac{3 43 \times 3 36}{2 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

343 \times 336

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

3 43 \times 36

Calculate the product

31548

\frac{3 1548}{2 3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

236 \times 3 6^{2}

Multiply the terms

2 \times 6

Multiply the terms

12

\frac{3 1548}{12}

x = \frac{3 1548}{12}

Alternative Form

x \approx 0.963997

Show Solution