Solve 3/4 -x( 1/2 - 5/8 ) ( (-3)/8 x)

Question

Simplify the expression

\frac{3}{4} - \frac{3}{64} x^{2}

Evaluate

\frac{3}{4} - x (\frac{1}{2} - \frac{5}{8}) (\frac{- 3}{8} x)

Remove the parentheses

\frac{3}{4} - x (\frac{1}{2} - \frac{5}{8}) \times \frac{- 3}{8} x

Subtract the numbers

More Steps

Simplify

\frac{1}{2} - \frac{5}{8}

Reduce fractions to a common denominator

\frac{4}{2 \times 4} - \frac{5}{8}

Multiply the numbers

\frac{4}{8} - \frac{5}{8}

Write all numerators above the common denominator

\frac{4 - 5}{8}

Subtract the numbers

\frac{- 1}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{8}

\frac{3}{4} - x (- \frac{1}{8}) \times \frac{- 3}{8} x

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{3}{4} - x (- \frac{1}{8}) (- \frac{3}{8}) x

Solution

More Steps

Multiply the terms

x (- \frac{1}{8}) (- \frac{3}{8}) x

Rewrite the expression

x \times \frac{1}{8} \times \frac{3}{8} x

Multiply the terms

x^{2} \times \frac{1}{8} \times \frac{3}{8}

Multiply the terms

More Steps

Evaluate

\frac{1}{8} \times \frac{3}{8}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3}{8 \times 8}

Multiply the numbers

\frac{3}{64}

x^{2} \times \frac{3}{64}

Use the commutative property to reorder the terms

\frac{3}{64} x^{2}

\frac{3}{4} - \frac{3}{64} x^{2}

Show Solution

Factor the expression

\frac{3}{64} (4 - x) (4 + x)

Evaluate

\frac{3}{4} - x (\frac{1}{2} - \frac{5}{8}) (\frac{- 3}{8} x)

Evaluate

More Steps

Evaluate

x (\frac{1}{2} - \frac{5}{8}) (\frac{- 3}{8} x)

Remove the parentheses

x (\frac{1}{2} - \frac{5}{8}) \times \frac{- 3}{8} x

Subtract the numbers

More Steps

Simplify

\frac{1}{2} - \frac{5}{8}

Reduce fractions to a common denominator

\frac{4}{2 \times 4} - \frac{5}{8}

Multiply the numbers

\frac{4}{8} - \frac{5}{8}

Write all numerators above the common denominator

\frac{4 - 5}{8}

Subtract the numbers

\frac{- 1}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{8}

x (- \frac{1}{8}) \times \frac{- 3}{8} x

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x (- \frac{1}{8}) (- \frac{3}{8}) x

Rewrite the expression

x \times \frac{1}{8} \times \frac{3}{8} x

Multiply the terms

x^{2} \times \frac{1}{8} \times \frac{3}{8}

Multiply the terms

More Steps

Evaluate

\frac{1}{8} \times \frac{3}{8}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3}{8 \times 8}

Multiply the numbers

\frac{3}{64}

x^{2} \times \frac{3}{64}

Use the commutative property to reorder the terms

\frac{3}{64} x^{2}

\frac{3}{4} - \frac{3}{64} x^{2}

Factor out \frac{3}{64} from the expression

\frac{3}{64} (16 - x^{2})

Solution

More Steps

Evaluate

16 - x^{2}

Rewrite the expression in exponential form

4^{2} - x^{2}

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

(4 - x) (4 + x)

\frac{3}{64} (4 - x) (4 + x)

Show Solution

Find the roots

x_{1} = - 4, x_{2} = 4

Evaluate

\frac{3}{4} - x (\frac{1}{2} - \frac{5}{8}) (\frac{- 3}{8} x)

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

\frac{3}{4} - x (\frac{1}{2} - \frac{5}{8}) (\frac{- 3}{8} x) = 0

Subtract the numbers

More Steps

Simplify

\frac{1}{2} - \frac{5}{8}

Reduce fractions to a common denominator

\frac{4}{2 \times 4} - \frac{5}{8}

Multiply the numbers

\frac{4}{8} - \frac{5}{8}

Write all numerators above the common denominator

\frac{4 - 5}{8}

Subtract the numbers

\frac{- 1}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{8}

\frac{3}{4} - x (- \frac{1}{8}) (\frac{- 3}{8} x) = 0

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{3}{4} - x (- \frac{1}{8}) (- \frac{3}{8} x) = 0

Multiply

More Steps

Multiply the terms

x (- \frac{1}{8}) (- \frac{3}{8} x)

Rewrite the expression

x \times \frac{1}{8} \times \frac{3}{8} x

Multiply the terms

x^{2} \times \frac{1}{8} \times \frac{3}{8}

Multiply the terms

More Steps

Evaluate

\frac{1}{8} \times \frac{3}{8}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3}{8 \times 8}

Multiply the numbers

\frac{3}{64}

x^{2} \times \frac{3}{64}

Use the commutative property to reorder the terms

\frac{3}{64} x^{2}

\frac{3}{4} - \frac{3}{64} x^{2} = 0

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

- \frac{3}{64} x^{2} = 0 - \frac{3}{4}

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

- \frac{3}{64} x^{2} = - \frac{3}{4}

Change the signs on both sides of the equation

\frac{3}{64} x^{2} = \frac{3}{4}

Multiply by the reciprocal

\frac{3}{64} x^{2} \times \frac{64}{3} = \frac{3}{4} \times \frac{64}{3}

Multiply

x^{2} = \frac{3}{4} \times \frac{64}{3}

Multiply

More Steps

Evaluate

\frac{3}{4} \times \frac{64}{3}

Reduce the numbers

\frac{1}{4} \times 64

Reduce the numbers

1 \times 16

Simplify

16

x^{2} = 16

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

x = \pm 16

Simplify the expression

More Steps

Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

x = \pm 4

Separate the equation into 2 possible cases

x = 4 x = - 4

Solution

x_{1} = - 4, x_{2} = 4

Show Solution