Solve 2x^2 +7x -4

Question

Factor the expression

(x + 4) (2 x - 1)

Evaluate

2 x^{2} + 7 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} + 7 x - 4

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

2 x^{2} + 7 x - 4 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + 7 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}

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