Solve 20x^(2)-1x_( 10)=0

Question

Solve the equation

Solve for x

Solve for x_{10}

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

Evaluate

20 x^{2} - 1 \times x_{10} = 0

Any expression multiplied by 1 remains the same

20 x^{2} - x_{10} = 0

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

20 x^{2} = 0 + x_{10}

Add the terms

20 x^{2} = x_{10}

Divide both sides

\frac{20 x ^{2}}{20} = \frac{x _{10}}{20}

Divide the numbers

x^{2} = \frac{x _{10}}{20}

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

x = \pm \frac{x _{10}}{20}

Simplify the expression

More Steps

Evaluate

\frac{x _{10}}{20}

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

\frac{x _{10}}{20}

Simplify the radical expression

More Steps

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{x _{10}}{2 5}

Multiply by the Conjugate

\frac{x _{10} \times 5}{2 5 \times 5}

Calculate

\frac{x _{10} \times 5}{2 \times 5}

Calculate

More Steps

Evaluate

x_{10} \times 5

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

x_{10} \times 5

Calculate the product

5 x_{10}

\frac{5 x _{10}}{2 \times 5}

Calculate

\frac{5 x _{10}}{10}

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

Solution

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

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