Solve 10x 12x - 6

Question

Simplify the expression

120 x^{2} - 6

Evaluate

10 x \times 12 x - 6

Solution

More Steps

Evaluate

10 x \times 12 x

Multiply the terms

120 x \times x

Multiply the terms

120 x^{2}

120 x^{2} - 6

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Factor the expression

6 (20 x^{2} - 1)

Evaluate

10 x \times 12 x - 6

Multiply

More Steps

Evaluate

10 x \times 12 x

Multiply the terms

120 x \times x

Multiply the terms

120 x^{2}

120 x^{2} - 6

Solution

6 (20 x^{2} - 1)

Show Solution

Find the roots

x_{1} = - \frac{5}{10}, x_{2} = \frac{5}{10}

Alternative Form

x_{1} \approx - 0.223607, x_{2} \approx 0.223607

Evaluate

10 x \times 12 x - 6

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

10 x \times 12 x - 6 = 0

Multiply

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Multiply the terms

10 x \times 12 x

Multiply the terms

120 x \times x

Multiply the terms

120 x^{2}

120 x^{2} - 6 = 0

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

120 x^{2} = 0 + 6

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

120 x^{2} = 6

Divide both sides

\frac{120 x ^{2}}{120} = \frac{6}{120}

Divide the numbers

x^{2} = \frac{6}{120}

Cancel out the common factor 6

x^{2} = \frac{1}{20}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{1}{20}

Simplify the expression

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Evaluate

\frac{1}{20}

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

\frac{1}{20}

Simplify the radical expression

\frac{1}{20}

Simplify the radical expression

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Evaluate

20

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

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

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

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

\frac{1}{2 5}

Multiply by the Conjugate

\frac{5}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

25 \times 5

When a square root of an expression is multiplied by itself,the result is that expression

2 \times 5

Multiply the terms

10

\frac{5}{10}

x = \pm \frac{5}{10}

Separate the equation into 2 possible cases

x = \frac{5}{10} x = - \frac{5}{10}

Solution

x_{1} = - \frac{5}{10}, x_{2} = \frac{5}{10}

Alternative Form

x_{1} \approx - 0.223607, x_{2} \approx 0.223607

Show Solution