Solve 4x 166x - 6

Question

Simplify the expression

664 x^{2} - 6

Evaluate

4 x \times 166 x - 6

Solution

More Steps

Evaluate

4 x \times 166 x

Multiply the terms

664 x \times x

Multiply the terms

664 x^{2}

664 x^{2} - 6

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Factor the expression

2 (332 x^{2} - 3)

Evaluate

4 x \times 166 x - 6

Multiply

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Evaluate

4 x \times 166 x

Multiply the terms

664 x \times x

Multiply the terms

664 x^{2}

664 x^{2} - 6

Solution

2 (332 x^{2} - 3)

Show Solution

Find the roots

x_{1} = - \frac{249}{166}, x_{2} = \frac{249}{166}

Alternative Form

x_{1} \approx - 0.095059, x_{2} \approx 0.095059

Evaluate

4 x \times 166 x - 6

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

4 x \times 166 x - 6 = 0

Multiply

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Multiply the terms

4 x \times 166 x

Multiply the terms

664 x \times x

Multiply the terms

664 x^{2}

664 x^{2} - 6 = 0

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

664 x^{2} = 0 + 6

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

664 x^{2} = 6

Divide both sides

\frac{664 x ^{2}}{664} = \frac{6}{664}

Divide the numbers

x^{2} = \frac{6}{664}

Cancel out the common factor 2

x^{2} = \frac{3}{332}

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

x = \pm \frac{3}{332}

Simplify the expression

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Evaluate

\frac{3}{332}

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

\frac{3}{332}

Simplify the radical expression

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Evaluate

332

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

4 \times 83

Write the number in exponential form with the base of 2

2^{2} \times 83

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

2^{2} \times 83

Reduce the index of the radical and exponent with 2

283

\frac{3}{2 83}

Multiply by the Conjugate

\frac{3 \times 83}{2 83 \times 83}

Multiply the numbers

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Evaluate

3 \times 83

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

3 \times 83

Calculate the product

249

\frac{249}{2 83 \times 83}

Multiply the numbers

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Evaluate

283 \times 83

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

2 \times 83

Multiply the terms

166

\frac{249}{166}

x = \pm \frac{249}{166}

Separate the equation into 2 possible cases

x = \frac{249}{166} x = - \frac{249}{166}

Solution

x_{1} = - \frac{249}{166}, x_{2} = \frac{249}{166}

Alternative Form

x_{1} \approx - 0.095059, x_{2} \approx 0.095059

Show Solution