Solve (x (4-x)i-3 i)/1 /(2i-3 i)

Question

Simplify the expression

- 4 x + x^{2} + 3

Evaluate

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

Remove the parentheses

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

Use the commutative property to reorder the terms

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

Expand the expression

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Simplify

i x (4 - x) - 3 i

Expand the expression

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Evaluate

i x (4 - x)

Apply the distributive property

i x \times 4 - i x \times x

Multiply the numbers

4 i x - i x \times x

Multiply the terms

4 i x - i x^{2}

4 i x - i x^{2} - 3 i

\frac{\frac{4 i x - i x ^{2} - 3 i}{1}}{2 i - 3 i}

Divide the terms

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

Subtract the numbers

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Simplify

2 i - 3 i

Collect like terms

(2 - 3) i

Calculate

- i

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

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

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

Multiply numerator and denominator by conjugate of denominator

- \frac{( 4 i x - i x ^{2} - 3 i ) i}{i \times i}

Simplify the expression

- \frac{i ( 4 i x - i x ^{2} - 3 i )}{i \times i}

Simplify the expression

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Evaluate

i \times i

Multiply

i^{2}

Use i^{2} = - 1 to transform the expression

1 \times (- 1)

Calculate

- 1

- \frac{i ( 4 i x - i x ^{2} - 3 i )}{- 1}

Divide the terms

i (4 i x - i x^{2} - 3 i)

Apply the distributive property

i \times 4 i x - i \times i x^{2} - i \times 3 i

Multiply the numbers

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Evaluate

i \times 4 i

Multiply

4 i^{2}

Use i^{2} = - 1 to transform the expression

4 (- 1)

Calculate

- 4

- 4 x - i \times i x^{2} - i \times 3 i

Multiply the numbers

More Steps

Evaluate

i \times i

Multiply

i^{2}

Use i^{2} = - 1 to transform the expression

1 \times (- 1)

Calculate

- 1

- 4 x - (- x^{2}) - i \times 3 i

Multiply the numbers

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Evaluate

i \times 3 i

Multiply

3 i^{2}

Use i^{2} = - 1 to transform the expression

3 (- 1)

Calculate

- 3

- 4 x - (- x^{2}) - (- 3)

Solution

- 4 x + x^{2} + 3

Show Solution

Find the roots

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

Evaluate

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

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

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

Subtract the numbers

More Steps

Simplify

2 i - 3 i

Collect like terms

(2 - 3) i

Calculate

- i

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

Remove the parentheses

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

Use the commutative property to reorder the terms

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

Expand the expression

More Steps

Simplify

i x (4 - x) - 3 i

Expand the expression

More Steps

Evaluate

i x (4 - x)

Apply the distributive property

i x \times 4 - i x \times x

Multiply the numbers

4 i x - i x \times x

Multiply the terms

4 i x - i x^{2}

4 i x - i x^{2} - 3 i

\frac{\frac{4 i x - i x ^{2} - 3 i}{1}}{- i} = 0

Divide the terms

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

Divide the terms

More Steps

Evaluate

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

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

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

Multiply numerator and denominator by conjugate of denominator

- \frac{( 4 i x - i x ^{2} - 3 i ) i}{i \times i}

Simplify the expression

- \frac{i ( 4 i x - i x ^{2} - 3 i )}{i \times i}

Simplify the expression

More Steps

Evaluate

i \times i

Multiply

i^{2}

Use i^{2} = - 1 to transform the expression

1 \times (- 1)

Calculate

- 1

- \frac{i ( 4 i x - i x ^{2} - 3 i )}{- 1}

Divide the terms

i (4 i x - i x^{2} - 3 i)

i (4 i x - i x^{2} - 3 i) = 0

Expand the expression

More Steps

Evaluate

i (4 i x - i x^{2} - 3 i)

Apply the distributive property

i \times 4 i x - i \times i x^{2} - i \times 3 i

Multiply the numbers

More Steps

Evaluate

i \times 4 i

Multiply

4 i^{2}

Use i^{2} = - 1 to transform the expression

4 (- 1)

Calculate

- 4

- 4 x - i \times i x^{2} - i \times 3 i

Multiply the numbers

More Steps

Evaluate

i \times i

Multiply

i^{2}

Use i^{2} = - 1 to transform the expression

1 \times (- 1)

Calculate

- 1

- 4 x - (- x^{2}) - i \times 3 i

Multiply the numbers

More Steps

Evaluate

i \times 3 i

Multiply

3 i^{2}

Use i^{2} = - 1 to transform the expression

3 (- 1)

Calculate

- 3

- 4 x - (- x^{2}) - (- 3)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 4 x + x^{2} + 3

- 4 x + x^{2} + 3 = 0

Factor the expression

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Evaluate

- 4 x + x^{2} + 3

Reorder the terms

x^{2} - 4 x + 3

Rewrite the expression

x^{2} + (- 1 - 3) x + 3

Calculate

x^{2} - x - 3 x + 3

Rewrite the expression

x \times x - x - 3 x + 3

Factor out x from the expression

x (x - 1) - 3 x + 3

Factor out - 3 from the expression

x (x - 1) - 3 (x - 1)

Factor out x - 1 from the expression

(x - 3) (x - 1)

(x - 3) (x - 1) = 0

When the product of factors equals 0,at least one factor is 0

x - 3 = 0 x - 1 = 0

Solve the equation for x

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Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 x - 1 = 0

Solve the equation for x

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Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 3 x = 1

Solution

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

Show Solution