Solve 2x^2-3x-14 - ScanMath

Question

Factor the expression

(x + 2) (2 x - 7)

Evaluate

2 x^{2} - 3 x - 14

Rewrite the expression

2 x^{2} + (- 7 + 4) x - 14

Calculate

2 x^{2} - 7 x + 4 x - 14

Rewrite the expression

x \times 2 x - x \times 7 + 2 \times 2 x - 2 \times 7

Factor out x from the expression

x (2 x - 7) + 2 \times 2 x - 2 \times 7

Factor out 2 from the expression

x (2 x - 7) + 2 (2 x - 7)

Solution

(x + 2) (2 x - 7)

Show Solution

x_{1} = - 2, x_{2} = \frac{7}{2}

Alternative Form

x_{1} = - 2, x_{2} = 3.5

Evaluate

2 x^{2} - 3 x - 14

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

2 x^{2} - 3 x - 14 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 3 x - 14

Rewrite the expression

2 x^{2} + (- 7 + 4) x - 14

Calculate

2 x^{2} - 7 x + 4 x - 14

Rewrite the expression

x \times 2 x - x \times 7 + 2 \times 2 x - 2 \times 7

Factor out x from the expression

x (2 x - 7) + 2 \times 2 x - 2 \times 7

Factor out 2 from the expression

x (2 x - 7) + 2 (2 x - 7)

Factor out 2 x - 7 from the expression

(x + 2) (2 x - 7)

(x + 2) (2 x - 7) = 0

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

x + 2 = 0 2 x - 7 = 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 - 7 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 7 = 0

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

2 x = 0 + 7

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

2 x = 7

Divide both sides

\frac{2 x}{2} = \frac{7}{2}

Divide the numbers

x = \frac{7}{2}

x = - 2 x = \frac{7}{2}

Solution

x_{1} = - 2, x_{2} = \frac{7}{2}

Alternative Form

x_{1} = - 2, x_{2} = 3.5

Show Solution