Solve 2x^2+7/2x+3/4

Question

Factor the expression

\frac{1}{4} (2 x + 3) (4 x + 1)

Evaluate

2 x^{2} + \frac{7}{2} x + \frac{3}{4}

Rewrite the expression

\frac{1}{4} \times 8 x^{2} + \frac{1}{4} \times 14 x + \frac{1}{4} \times 3

Factor out \frac{1}{4} from the expression

\frac{1}{4} (8 x^{2} + 14 x + 3)

Solution

More Steps

Evaluate

8 x^{2} + 14 x + 3

Rewrite the expression

8 x^{2} + (2 + 12) x + 3

Calculate

8 x^{2} + 2 x + 12 x + 3

Rewrite the expression

2 x \times 4 x + 2 x + 3 \times 4 x + 3

Factor out 2 x from the expression

2 x (4 x + 1) + 3 \times 4 x + 3

Factor out 3 from the expression

2 x (4 x + 1) + 3 (4 x + 1)

Factor out 4 x + 1 from the expression

(2 x + 3) (4 x + 1)

\frac{1}{4} (2 x + 3) (4 x + 1)

Show Solution

x_{1} = - \frac{3}{2}, x_{2} = - \frac{1}{4}

Alternative Form

x_{1} = - 1.5, x_{2} = - 0.25

Evaluate

2 x^{2} + \frac{7}{2} x + \frac{3}{4}

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

2 x^{2} + \frac{7}{2} x + \frac{3}{4} = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + \frac{7}{2} x + \frac{3}{4}

Rewrite the expression

\frac{1}{4} \times 8 x^{2} + \frac{1}{4} \times 14 x + \frac{1}{4} \times 3

Factor out \frac{1}{4} from the expression

\frac{1}{4} (8 x^{2} + 14 x + 3)

Factor the expression

More Steps

Evaluate

8 x^{2} + 14 x + 3

Rewrite the expression

8 x^{2} + (2 + 12) x + 3

Calculate

8 x^{2} + 2 x + 12 x + 3

Rewrite the expression

2 x \times 4 x + 2 x + 3 \times 4 x + 3

Factor out 2 x from the expression

2 x (4 x + 1) + 3 \times 4 x + 3

Factor out 3 from the expression

2 x (4 x + 1) + 3 (4 x + 1)

Factor out 4 x + 1 from the expression

(2 x + 3) (4 x + 1)

\frac{1}{4} (2 x + 3) (4 x + 1)

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

Divide the terms

(2 x + 3) (4 x + 1) = 0

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

2 x + 3 = 0 4 x + 1 = 0

Solve the equation for x

More Steps

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}

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

x = - \frac{3}{2}

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

Solve the equation for x

More Steps

Evaluate

4 x + 1 = 0

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

4 x = 0 - 1

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

4 x = - 1

Divide both sides

\frac{4 x}{4} = \frac{- 1}{4}

Divide the numbers

x = \frac{- 1}{4}

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

x = - \frac{1}{4}

x = - \frac{3}{2} x = - \frac{1}{4}

Solution

x_{1} = - \frac{3}{2}, x_{2} = - \frac{1}{4}

Alternative Form

x_{1} = - 1.5, x_{2} = - 0.25

Show Solution