Solve 7x^2+38x+40

Question

Factor the expression

(x + 4) (7 x + 10)

Evaluate

7 x^{2} + 38 x + 40

Rewrite the expression

7 x^{2} + (10 + 28) x + 40

Calculate

7 x^{2} + 10 x + 28 x + 40

Rewrite the expression

x \times 7 x + x \times 10 + 4 \times 7 x + 4 \times 10

Factor out x from the expression

x (7 x + 10) + 4 \times 7 x + 4 \times 10

Factor out 4 from the expression

x (7 x + 10) + 4 (7 x + 10)

Solution

(x + 4) (7 x + 10)

Show Solution

x_{1} = - 4, x_{2} = - \frac{10}{7}

Alternative Form

x_{1} = - 4, x_{2} = - 1. \dot{4} 2857 \dot{1}

Evaluate

7 x^{2} + 38 x + 40

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

7 x^{2} + 38 x + 40 = 0

Factor the expression

More Steps

Evaluate

7 x^{2} + 38 x + 40

Rewrite the expression

7 x^{2} + (10 + 28) x + 40

Calculate

7 x^{2} + 10 x + 28 x + 40

Rewrite the expression

x \times 7 x + x \times 10 + 4 \times 7 x + 4 \times 10

Factor out x from the expression

x (7 x + 10) + 4 \times 7 x + 4 \times 10

Factor out 4 from the expression

x (7 x + 10) + 4 (7 x + 10)

Factor out 7 x + 10 from the expression

(x + 4) (7 x + 10)

(x + 4) (7 x + 10) = 0

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

x + 4 = 0 7 x + 10 = 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 7 x + 10 = 0

Solve the equation for x

More Steps

Evaluate

7 x + 10 = 0

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

7 x = 0 - 10

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

7 x = - 10

Divide both sides

\frac{7 x}{7} = \frac{- 10}{7}

Divide the numbers

x = \frac{- 10}{7}

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

x = - \frac{10}{7}

x = - 4 x = - \frac{10}{7}

Solution

x_{1} = - 4, x_{2} = - \frac{10}{7}

Alternative Form

x_{1} = - 4, x_{2} = - 1. \dot{4} 2857 \dot{1}

Show Solution