Solve x^2 - 3/2x-1

Question

Factor the expression

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

Evaluate

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

Rewrite the expression

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

Factor out \frac{1}{2} from the expression

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

Solution

More Steps

Evaluate

2 x^{2} - 3 x - 2

Rewrite the expression

2 x^{2} + (1 - 4) x - 2

Calculate

2 x^{2} + x - 4 x - 2

Rewrite the expression

x \times 2 x + x - 2 \times 2 x - 2

Factor out x from the expression

x (2 x + 1) - 2 \times 2 x - 2

Factor out - 2 from the expression

x (2 x + 1) - 2 (2 x + 1)

Factor out 2 x + 1 from the expression

(x - 2) (2 x + 1)

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

Show Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 2

Evaluate

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

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

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

Factor the expression

More Steps

Evaluate

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

Rewrite the expression

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

Factor out \frac{1}{2} from the expression

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

Factor the expression

More Steps

Evaluate

2 x^{2} - 3 x - 2

Rewrite the expression

2 x^{2} + (1 - 4) x - 2

Calculate

2 x^{2} + x - 4 x - 2

Rewrite the expression

x \times 2 x + x - 2 \times 2 x - 2

Factor out x from the expression

x (2 x + 1) - 2 \times 2 x - 2

Factor out - 2 from the expression

x (2 x + 1) - 2 (2 x + 1)

Factor out 2 x + 1 from the expression

(x - 2) (2 x + 1)

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

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

Divide the terms

(x - 2) (2 x + 1) = 0

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

x - 2 = 0 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 2 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 1 = 0

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

2 x = 0 - 1

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

2 x = - 1

Divide both sides

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

Divide the numbers

x = \frac{- 1}{2}

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

x = - \frac{1}{2}

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

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 2

Show Solution