Solve 5x 1910x - 14

Question

Simplify the expression

9550 x^{2} - 14

Evaluate

5 x \times 1910 x - 14

Solution

More Steps

Evaluate

5 x \times 1910 x

Multiply the terms

9550 x \times x

Multiply the terms

9550 x^{2}

9550 x^{2} - 14

Show Solution

Factor the expression

2 (4775 x^{2} - 7)

Evaluate

5 x \times 1910 x - 14

Multiply

More Steps

Evaluate

5 x \times 1910 x

Multiply the terms

9550 x \times x

Multiply the terms

9550 x^{2}

9550 x^{2} - 14

Solution

2 (4775 x^{2} - 7)

Show Solution

Find the roots

x_{1} = - \frac{1337}{955}, x_{2} = \frac{1337}{955}

Alternative Form

x_{1} \approx - 0.038288, x_{2} \approx 0.038288

Evaluate

5 x \times 1910 x - 14

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

5 x \times 1910 x - 14 = 0

Multiply

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Multiply the terms

5 x \times 1910 x

Multiply the terms

9550 x \times x

Multiply the terms

9550 x^{2}

9550 x^{2} - 14 = 0

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

9550 x^{2} = 0 + 14

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

9550 x^{2} = 14

Divide both sides

\frac{9550 x ^{2}}{9550} = \frac{14}{9550}

Divide the numbers

x^{2} = \frac{14}{9550}

Cancel out the common factor 2

x^{2} = \frac{7}{4775}

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

x = \pm \frac{7}{4775}

Simplify the expression

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Evaluate

\frac{7}{4775}

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

\frac{7}{4775}

Simplify the radical expression

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Evaluate

4775

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

25 \times 191

Write the number in exponential form with the base of 5

5^{2} \times 191

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

5^{2} \times 191

Reduce the index of the radical and exponent with 2

5191

\frac{7}{5 191}

Multiply by the Conjugate

\frac{7 \times 191}{5 191 \times 191}

Multiply the numbers

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Evaluate

7 \times 191

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

7 \times 191

Calculate the product

1337

\frac{1337}{5 191 \times 191}

Multiply the numbers

More Steps

Evaluate

5191 \times 191

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

5 \times 191

Multiply the terms

955

\frac{1337}{955}

x = \pm \frac{1337}{955}

Separate the equation into 2 possible cases

x = \frac{1337}{955} x = - \frac{1337}{955}

Solution

x_{1} = - \frac{1337}{955}, x_{2} = \frac{1337}{955}

Alternative Form

x_{1} \approx - 0.038288, x_{2} \approx 0.038288

Show Solution