Solve (x 1/100)^2-1/100 9/100

Question

Simplify the expression

\frac{1}{10000} x^{2} - \frac{9}{10000}

Evaluate

(x \times \frac{1}{100})^{2} - \frac{1}{100} \times \frac{9}{100}

Use the commutative property to reorder the terms

(\frac{1}{100} x)^{2} - \frac{1}{100} \times \frac{9}{100}

Multiply the numbers

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Evaluate

\frac{1}{100} \times \frac{9}{100}

To multiply the fractions,multiply the numerators and denominators separately

\frac{9}{100 \times 100}

Multiply the numbers

\frac{9}{10000}

(\frac{1}{100} x)^{2} - \frac{9}{10000}

Solution

\frac{1}{10000} x^{2} - \frac{9}{10000}

Show Solution

Factor the expression

\frac{1}{10000} (x - 3) (x + 3)

Evaluate

(x \times \frac{1}{100})^{2} - \frac{1}{100} \times \frac{9}{100}

Evaluate

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Evaluate

(x \times \frac{1}{100})^{2}

Use the commutative property to reorder the terms

(\frac{1}{100} x)^{2}

To raise a product to a power,raise each factor to that power

(\frac{1}{100})^{2} x^{2}

Evaluate the power

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Evaluate

(\frac{1}{100})^{2}

To raise a fraction to a power,raise the numerator and denominator to that power

\frac{1 ^{2}}{10 0 ^{2}}

Evaluate the power

\frac{1}{10 0 ^{2}}

Evaluate the power

\frac{1}{10000}

\frac{1}{10000} x^{2}

\frac{1}{10000} x^{2} - \frac{1}{100} \times \frac{9}{100}

Evaluate

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Evaluate

\frac{1}{100} \times \frac{9}{100}

To multiply the fractions,multiply the numerators and denominators separately

\frac{9}{100 \times 100}

Multiply the numbers

\frac{9}{10000}

\frac{1}{10000} x^{2} - \frac{9}{10000}

Factor out \frac{1}{10000} from the expression

\frac{1}{10000} (x^{2} - 9)

Solution

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Evaluate

x^{2} - 9

Rewrite the expression in exponential form

x^{2} - 3^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(x - 3) (x + 3)

\frac{1}{10000} (x - 3) (x + 3)

Show Solution

Find the roots

x_{1} = - 3, x_{2} = 3

Evaluate

(x \times \frac{1}{100})^{2} - \frac{1}{100} \times \frac{9}{100}

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

(x \times \frac{1}{100})^{2} - \frac{1}{100} \times \frac{9}{100} = 0

Use the commutative property to reorder the terms

(\frac{1}{100} x)^{2} - \frac{1}{100} \times \frac{9}{100} = 0

Multiply the numbers

More Steps

Evaluate

\frac{1}{100} \times \frac{9}{100}

To multiply the fractions,multiply the numerators and denominators separately

\frac{9}{100 \times 100}

Multiply the numbers

\frac{9}{10000}

(\frac{1}{100} x)^{2} - \frac{9}{10000} = 0

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

(\frac{1}{100} x)^{2} = 0 + \frac{9}{10000}

Add the terms

(\frac{1}{100} x)^{2} = \frac{9}{10000}

Calculate

\frac{1}{10000} x^{2} = \frac{9}{10000}

Multiply by the reciprocal

\frac{1}{10000} x^{2} \times 10000 = \frac{9}{10000} \times 10000

Multiply

x^{2} = \frac{9}{10000} \times 10000

Multiply

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Evaluate

\frac{9}{10000} \times 10000

Reduce the numbers

9 \times 1

Simplify

9

x^{2} = 9

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

x = \pm 9

Simplify the expression

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Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

x = \pm 3

Separate the equation into 2 possible cases

x = 3 x = - 3

Solution

x_{1} = - 3, x_{2} = 3

Show Solution