Solve 9x^2 14x - 254/100 = 0

Question

Solve the equation

x = \frac{3 127 \times 630 0 ^{2}}{6300}

Alternative Form

x \approx 0.272158

Evaluate

9 x^{2} \times 14 x - \frac{254}{100} = 0

Simplify

More Steps

Evaluate

9 x^{2} \times 14 x - \frac{254}{100}

Cancel out the common factor 2

9 x^{2} \times 14 x - \frac{127}{50}

Multiply

More Steps

Multiply the terms

9 x^{2} \times 14 x

Multiply the terms

126 x^{2} \times x

Multiply the terms with the same base by adding their exponents

126 x^{2 + 1}

Add the numbers

126 x^{3}

126 x^{3} - \frac{127}{50}

126 x^{3} - \frac{127}{50} = 0

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

126 x^{3} = 0 + \frac{127}{50}

Add the terms

126 x^{3} = \frac{127}{50}

Multiply by the reciprocal

126 x^{3} \times \frac{1}{126} = \frac{127}{50} \times \frac{1}{126}

Multiply

x^{3} = \frac{127}{50} \times \frac{1}{126}

Multiply

More Steps

Evaluate

\frac{127}{50} \times \frac{1}{126}

To multiply the fractions,multiply the numerators and denominators separately

\frac{127}{50 \times 126}

Multiply the numbers

\frac{127}{6300}

x^{3} = \frac{127}{6300}

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

3 x^{3} = 3 \frac{127}{6300}

Calculate

x = 3 \frac{127}{6300}

Solution

More Steps

Evaluate

3 \frac{127}{6300}

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

\frac{3 127}{3 6300}

Multiply by the Conjugate

\frac{3 127 \times 3 630 0 ^{2}}{3 6300 \times 3 630 0 ^{2}}

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

\frac{3 127 \times 630 0 ^{2}}{3 6300 \times 3 630 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

36300 \times 3 630 0^{2}

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

3 6300 \times 630 0^{2}

Calculate the product

3 630 0^{3}

Reduce the index of the radical and exponent with 3

6300

\frac{3 127 \times 630 0 ^{2}}{6300}

x = \frac{3 127 \times 630 0 ^{2}}{6300}

Alternative Form

x \approx 0.272158

Show Solution