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

Question

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

Simplify the expression

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

Evaluate

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

Use the commutative property to reorder the terms

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

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}

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

Rewrite the expression

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

Apply the distributive property

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

Multiply the numbers

More Steps

Evaluate

100 \times \frac{1}{10000}

Reduce the numbers

1 \times \frac{1}{100}

Multiply the numbers

\frac{1}{100}

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

Solution

More Steps

Evaluate

100 \times \frac{9}{10000}

Reduce the numbers

1 \times \frac{9}{100}

Multiply the numbers

\frac{9}{100}

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

Show Solution

Factor the expression

\frac{1}{100} (x - 3) (x + 3)

Evaluate

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

Use the commutative property to reorder the terms

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

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}

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

Multiply the terms

More Steps

Evaluate

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

Rewrite the expression

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

Simplify

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

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

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

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

Solution

\frac{1}{100} (x - 3) (x + 3)

Show Solution

Find the roots

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

Evaluate

100 ((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

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

Use the commutative property to reorder the terms

100 ((\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}

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

Rewrite the expression

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

Multiply the terms

More Steps

Evaluate

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

Apply the distributive property

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

Multiply the numbers

More Steps

Evaluate

100 \times \frac{1}{10000}

Reduce the numbers

1 \times \frac{1}{100}

Multiply the numbers

\frac{1}{100}

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

Multiply the numbers

More Steps

Evaluate

100 \times \frac{9}{10000}

Reduce the numbers

1 \times \frac{9}{100}

Multiply the numbers

\frac{9}{100}

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

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

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

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

Add the terms

\frac{1}{100} x^{2} = \frac{9}{100}

Multiply by the reciprocal

\frac{1}{100} x^{2} \times 100 = \frac{9}{100} \times 100

Multiply

x^{2} = \frac{9}{100} \times 100

Multiply

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Evaluate

\frac{9}{100} \times 100

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

More Steps

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