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

Question

Simplify the expression

2 x^{2} - 3 x - 14

Evaluate

(x + 2) (2 x - 7)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

2 x^{2} - x \times 7 + 2 \times 2 x - 2 \times 7

Use the commutative property to reorder the terms

2 x^{2} - 7 x + 2 \times 2 x - 2 \times 7

Multiply the numbers

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

Multiply the numbers

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

Solution

More Steps

Evaluate

- 7 x + 4 x

Collect like terms by calculating the sum or difference of their coefficients

(- 7 + 4) x

Add the numbers

- 3 x

2 x^{2} - 3 x - 14

Show Solution

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

Alternative Form

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

Evaluate

(x + 2) (2 x - 7)

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

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

Separate the equation into 2 possible cases

x + 2 = 0 2 x - 7 = 0

Solve the equation

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

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