Solve 25x^2-16/15x^2 27x 12

Question

Simplify the expression

25 x^{2} - \frac{1728}{5} x^{3}

Evaluate

25 x^{2} - \frac{16}{15} x^{2} \times 27 x \times 12

Solution

More Steps

Evaluate

\frac{16}{15} x^{2} \times 27 x \times 12

Multiply the terms

More Steps

Evaluate

\frac{16}{15} \times 27 \times 12

Multiply the terms

\frac{144}{5} \times 12

Multiply the numbers

\frac{144 \times 12}{5}

Multiply the numbers

\frac{1728}{5}

\frac{1728}{5} x^{2} \times x

Multiply the terms with the same base by adding their exponents

\frac{1728}{5} x^{2 + 1}

Add the numbers

\frac{1728}{5} x^{3}

25 x^{2} - \frac{1728}{5} x^{3}

Show Solution

Factor the expression

\frac{1}{5} x^{2} (125 - 1728 x)

Evaluate

25 x^{2} - \frac{16}{15} x^{2} \times 27 x \times 12

Multiply

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Evaluate

\frac{16}{15} x^{2} \times 27 x \times 12

Multiply the terms

More Steps

Evaluate

\frac{16}{15} \times 27 \times 12

Multiply the terms

\frac{144}{5} \times 12

Multiply the numbers

\frac{144 \times 12}{5}

Multiply the numbers

\frac{1728}{5}

\frac{1728}{5} x^{2} \times x

Multiply the terms with the same base by adding their exponents

\frac{1728}{5} x^{2 + 1}

Add the numbers

\frac{1728}{5} x^{3}

25 x^{2} - \frac{1728}{5} x^{3}

Rewrite the expression

\frac{1}{5} x^{2} \times 125 - \frac{1}{5} x^{2} \times 1728 x

Solution

\frac{1}{5} x^{2} (125 - 1728 x)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{125}{1728}

Alternative Form

x_{1} = 0, x_{2} \approx 0.072338

Evaluate

25 x^{2} - \frac{16}{15} x^{2} \times 27 x \times 12

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

25 x^{2} - \frac{16}{15} x^{2} \times 27 x \times 12 = 0

Multiply

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Multiply the terms

\frac{16}{15} x^{2} \times 27 x \times 12

Multiply the terms

More Steps

Evaluate

\frac{16}{15} \times 27 \times 12

Multiply the terms

\frac{144}{5} \times 12

Multiply the numbers

\frac{144 \times 12}{5}

Multiply the numbers

\frac{1728}{5}

\frac{1728}{5} x^{2} \times x

Multiply the terms with the same base by adding their exponents

\frac{1728}{5} x^{2 + 1}

Add the numbers

\frac{1728}{5} x^{3}

25 x^{2} - \frac{1728}{5} x^{3} = 0

Factor the expression

x^{2} (25 - \frac{1728}{5} x) = 0

Separate the equation into 2 possible cases

x^{2} = 0 25 - \frac{1728}{5} x = 0

The only way a power can be 0 is when the base equals 0

x = 0 25 - \frac{1728}{5} x = 0

Solve the equation

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Evaluate

25 - \frac{1728}{5} x = 0

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

- \frac{1728}{5} x = 0 - 25

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

- \frac{1728}{5} x = - 25

Change the signs on both sides of the equation

\frac{1728}{5} x = 25

Multiply by the reciprocal

\frac{1728}{5} x \times \frac{5}{1728} = 25 \times \frac{5}{1728}

Multiply

x = 25 \times \frac{5}{1728}

Multiply

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Evaluate

25 \times \frac{5}{1728}

Multiply the numbers

\frac{25 \times 5}{1728}

Multiply the numbers

\frac{125}{1728}

x = \frac{125}{1728}

x = 0 x = \frac{125}{1728}

Solution

x_{1} = 0, x_{2} = \frac{125}{1728}

Alternative Form

x_{1} = 0, x_{2} \approx 0.072338

Show Solution