Solve 12x^2-x-6(6x)(-6x)

Question

Simplify the expression

228 x^{2} - x

Evaluate

12 x^{2} - x - 6 \times 6 x (- 6 x)

Multiply

More Steps

Multiply the terms

- 6 \times 6 x (- 6 x)

Rewrite the expression

6 \times 6 x \times 6 x

Multiply the terms with the same base by adding their exponents

6^{1 + 1 + 1} x \times x

Add the numbers

6^{3} x \times x

Multiply the terms

6^{3} x^{2}

12 x^{2} - x + 6^{3} x^{2}

Evaluate the power

12 x^{2} - x + 216 x^{2}

Solution

More Steps

Evaluate

12 x^{2} + 216 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(12 + 216) x^{2}

Add the numbers

228 x^{2}

228 x^{2} - x

Show Solution

Factor the expression

x (228 x - 1)

Evaluate

12 x^{2} - x - 6 \times 6 x (- 6 x)

Multiply

More Steps

Multiply the terms

6 \times 6 x (- 6 x)

Rewrite the expression

- 6 \times 6 x \times 6 x

Multiply the terms with the same base by adding their exponents

- 6^{1 + 1 + 1} x \times x

Add the numbers

- 6^{3} x \times x

Multiply the terms

- 6^{3} x^{2}

12 x^{2} - x - (- 6^{3} x^{2})

Rewrite the expression

12 x^{2} - x + 6^{3} x^{2}

Add the terms

More Steps

Evaluate

12 x^{2} + 6^{3} x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(12 + 6^{3}) x^{2}

Add the numbers

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Evaluate

12 + 6^{3}

Rewrite the expression

12 + 216

Add the numbers

228

228 x^{2}

228 x^{2} - x

Rewrite the expression

x \times 228 x - x

Solution

x (228 x - 1)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{1}{228}

Alternative Form

x_{1} = 0, x_{2} \approx 0.004386

Evaluate

12 x^{2} - x - 6 (6 x) (- 6 x)

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

12 x^{2} - x - 6 (6 x) (- 6 x) = 0

Multiply the terms

12 x^{2} - x - 6 \times 6 x (- 6 x) = 0

Multiply

More Steps

Multiply the terms

6 \times 6 x (- 6 x)

Rewrite the expression

- 6 \times 6 x \times 6 x

Multiply the terms with the same base by adding their exponents

- 6^{1 + 1 + 1} x \times x

Add the numbers

- 6^{3} x \times x

Multiply the terms

- 6^{3} x^{2}

12 x^{2} - x - (- 6^{3} x^{2}) = 0

Subtract the terms

More Steps

Simplify

12 x^{2} - x - (- 6^{3} x^{2})

Rewrite the expression

12 x^{2} - x + 6^{3} x^{2}

Evaluate the power

12 x^{2} - x + 216 x^{2}

Add the terms

More Steps

Evaluate

12 x^{2} + 216 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(12 + 216) x^{2}

Add the numbers

228 x^{2}

228 x^{2} - x

228 x^{2} - x = 0

Factor the expression

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Evaluate

228 x^{2} - x

Rewrite the expression

x \times 228 x - x

Factor out x from the expression

x (228 x - 1)

x (228 x - 1) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 228 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

228 x - 1 = 0

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

228 x = 0 + 1

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

228 x = 1

Divide both sides

\frac{228 x}{228} = \frac{1}{228}

Divide the numbers

x = \frac{1}{228}

x = 0 x = \frac{1}{228}

Solution

x_{1} = 0, x_{2} = \frac{1}{228}

Alternative Form

x_{1} = 0, x_{2} \approx 0.004386

Show Solution