Solve (1/2x-1)*(2x-3)

Question

Simplify the expression

x^{2} - \frac{7}{2} x + 3

Evaluate

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

Apply the distributive property

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

Multiply the terms

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Evaluate

\frac{1}{2} x \times 2 x

Multiply the numbers

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Evaluate

\frac{1}{2} \times 2

Reduce the numbers

1 \times 1

Simplify

1

x \times x

Multiply the terms

x^{2}

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

Multiply the numbers

x^{2} - \frac{3}{2} x - 2 x - (- 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

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

Solution

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Evaluate

- \frac{3}{2} x - 2 x

Collect like terms by calculating the sum or difference of their coefficients

(- \frac{3}{2} - 2) x

Subtract the numbers

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Evaluate

- \frac{3}{2} - 2

Reduce fractions to a common denominator

- \frac{3}{2} - \frac{2 \times 2}{2}

Write all numerators above the common denominator

\frac{- 3 - 2 \times 2}{2}

Multiply the numbers

\frac{- 3 - 4}{2}

Subtract the numbers

\frac{- 7}{2}

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

- \frac{7}{2}

- \frac{7}{2} x

x^{2} - \frac{7}{2} x + 3

Show Solution

Factor the expression

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

Evaluate

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

Solution

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

Show Solution

Find the roots

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

Alternative Form

x_{1} = 1.5, x_{2} = 2

Evaluate

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

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

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

Separate the equation into 2 possible cases

\frac{1}{2} x - 1 = 0 2 x - 3 = 0

Solve the equation

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Evaluate

\frac{1}{2} x - 1 = 0

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

\frac{1}{2} x = 0 + 1

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

\frac{1}{2} x = 1

Multiply by the reciprocal

\frac{1}{2} x \times 2 = 1 \times 2

Multiply

x = 1 \times 2

Any expression multiplied by 1 remains the same

x = 2

x = 2 2 x - 3 = 0

Solve the equation

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Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

\frac{2 x}{2} = \frac{3}{2}

Divide the numbers

x = \frac{3}{2}

x = 2 x = \frac{3}{2}

Solution

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

Alternative Form

x_{1} = 1.5, x_{2} = 2

Show Solution