Solve 7r^2 + 38r + 40

Question

Factor the expression

(r + 4) (7 r + 10)

Evaluate

7 r^{2} + 38 r + 40

Rewrite the expression

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

Calculate

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

Rewrite the expression

r \times 7 r + r \times 10 + 4 \times 7 r + 4 \times 10

Factor out r from the expression

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

Factor out 4 from the expression

r (7 r + 10) + 4 (7 r + 10)

Solution

(r + 4) (7 r + 10)

Show Solution

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

Alternative Form

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

Evaluate

7 r^{2} + 38 r + 40

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

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

Factor the expression

More Steps

Evaluate

7 r^{2} + 38 r + 40

Rewrite the expression

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

Calculate

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

Rewrite the expression

r \times 7 r + r \times 10 + 4 \times 7 r + 4 \times 10

Factor out r from the expression

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

Factor out 4 from the expression

r (7 r + 10) + 4 (7 r + 10)

Factor out 7 r + 10 from the expression

(r + 4) (7 r + 10)

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

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

r + 4 = 0 7 r + 10 = 0

Solve the equation for r

More Steps

Evaluate

r + 4 = 0

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

r = 0 - 4

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

r = - 4

r = - 4 7 r + 10 = 0

Solve the equation for r

More Steps

Evaluate

7 r + 10 = 0

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

7 r = 0 - 10

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

7 r = - 10

Divide both sides

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

Divide the numbers

r = \frac{- 10}{7}

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

r = - \frac{10}{7}

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

Solution

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

Alternative Form

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

Show Solution