Solve 2x^2+9x+4 - ScanMath

Question

Factor the expression

(x + 4) (2 x + 1)

Evaluate

2 x^{2} + 9 x + 4

Rewrite the expression

2 x^{2} + (1 + 8) x + 4

Calculate

2 x^{2} + x + 8 x + 4

Rewrite the expression

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

Factor out x from the expression

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

Factor out 4 from the expression

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

Solution

(x + 4) (2 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 4, x_{2} = - 0.5

Evaluate

2 x^{2} + 9 x + 4

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

2 x^{2} + 9 x + 4 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + 9 x + 4

Rewrite the expression

2 x^{2} + (1 + 8) x + 4

Calculate

2 x^{2} + x + 8 x + 4

Rewrite the expression

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

Factor out x from the expression

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

Factor out 4 from the expression

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

Factor out 2 x + 1 from the expression

(x + 4) (2 x + 1)

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

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

x + 4 = 0 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x + 4 = 0

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

x = 0 - 4

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

x = - 4

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

Solution

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

Alternative Form

x_{1} = - 4, x_{2} = - 0.5

Show Solution