Solve 2x^2 - 5x -700

Question

Factor the expression

(x - 20) (2 x + 35)

Evaluate

2 x^{2} - 5 x - 700

Rewrite the expression

2 x^{2} + (35 - 40) x - 700

Calculate

2 x^{2} + 35 x - 40 x - 700

Rewrite the expression

x \times 2 x + x \times 35 - 20 \times 2 x - 20 \times 35

Factor out x from the expression

x (2 x + 35) - 20 \times 2 x - 20 \times 35

Factor out - 20 from the expression

x (2 x + 35) - 20 (2 x + 35)

Solution

(x - 20) (2 x + 35)

Show Solution

x_{1} = - \frac{35}{2}, x_{2} = 20

Alternative Form

x_{1} = - 17.5, x_{2} = 20

Evaluate

2 x^{2} - 5 x - 700

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

2 x^{2} - 5 x - 700 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 5 x - 700

Rewrite the expression

2 x^{2} + (35 - 40) x - 700

Calculate

2 x^{2} + 35 x - 40 x - 700

Rewrite the expression

x \times 2 x + x \times 35 - 20 \times 2 x - 20 \times 35

Factor out x from the expression

x (2 x + 35) - 20 \times 2 x - 20 \times 35

Factor out - 20 from the expression

x (2 x + 35) - 20 (2 x + 35)

Factor out 2 x + 35 from the expression

(x - 20) (2 x + 35)

(x - 20) (2 x + 35) = 0

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

x - 20 = 0 2 x + 35 = 0

Solve the equation for x

More Steps

Evaluate

x - 20 = 0

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

x = 0 + 20

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

x = 20

x = 20 2 x + 35 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 35 = 0

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

2 x = 0 - 35

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

2 x = - 35

Divide both sides

\frac{2 x}{2} = \frac{- 35}{2}

Divide the numbers

x = \frac{- 35}{2}

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

x = - \frac{35}{2}

x = 20 x = - \frac{35}{2}

Solution

x_{1} = - \frac{35}{2}, x_{2} = 20

Alternative Form

x_{1} = - 17.5, x_{2} = 20

Show Solution