Solve (w+7)(w+1) = -5

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

w_{1} = - 6, w_{2} = - 2

Evaluate

(w + 7) (w + 1) = - 5

Expand the expression

More Steps

Evaluate

(w + 7) (w + 1)

Apply the distributive property

w \times w + w \times 1 + 7 w + 7 \times 1

Multiply the terms

w^{2} + w \times 1 + 7 w + 7 \times 1

Any expression multiplied by 1 remains the same

w^{2} + w + 7 w + 7 \times 1

Any expression multiplied by 1 remains the same

w^{2} + w + 7 w + 7

Add the terms

More Steps

Evaluate

w + 7 w

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

(1 + 7) w

Add the numbers

8 w

w^{2} + 8 w + 7

w^{2} + 8 w + 7 = - 5

Move the expression to the left side

w^{2} + 8 w + 12 = 0

Factor the expression

More Steps

Evaluate

w^{2} + 8 w + 12

Rewrite the expression

w^{2} + (6 + 2) w + 12

Calculate

w^{2} + 6 w + 2 w + 12

Rewrite the expression

w \times w + w \times 6 + 2 w + 2 \times 6

Factor out w from the expression

w (w + 6) + 2 w + 2 \times 6

Factor out 2 from the expression

w (w + 6) + 2 (w + 6)

Factor out w + 6 from the expression

(w + 2) (w + 6)

(w + 2) (w + 6) = 0

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

w + 2 = 0 w + 6 = 0

Solve the equation for w

More Steps

Evaluate

w + 2 = 0

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

w = 0 - 2

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

w = - 2

w = - 2 w + 6 = 0

Solve the equation for w

More Steps

Evaluate

w + 6 = 0

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

w = 0 - 6

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

w = - 6

w = - 2 w = - 6

Solution

w_{1} = - 6, w_{2} = - 2

Show Solution