Solve 2w^2 - 16w = 12w - 48

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

w_{1} = 2, w_{2} = 12

Evaluate

2 w^{2} - 16 w = 12 w - 48

Move the expression to the left side

2 w^{2} - 28 w + 48 = 0

Factor the expression

More Steps

Evaluate

2 w^{2} - 28 w + 48

Rewrite the expression

2 w^{2} - 2 \times 14 w + 2 \times 24

Factor out 2 from the expression

2 (w^{2} - 14 w + 24)

Factor the expression

More Steps

Evaluate

w^{2} - 14 w + 24

Rewrite the expression

w^{2} + (- 2 - 12) w + 24

Calculate

w^{2} - 2 w - 12 w + 24

Rewrite the expression

w \times w - w \times 2 - 12 w + 12 \times 2

Factor out w from the expression

w (w - 2) - 12 w + 12 \times 2

Factor out - 12 from the expression

w (w - 2) - 12 (w - 2)

Factor out w - 2 from the expression

(w - 12) (w - 2)

2 (w - 12) (w - 2)

2 (w - 12) (w - 2) = 0

Divide the terms

(w - 12) (w - 2) = 0

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

w - 12 = 0 w - 2 = 0

Solve the equation for w

More Steps

Evaluate

w - 12 = 0

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

w = 0 + 12

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

w = 12

w = 12 w - 2 = 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 = 12 w = 2

Solution

w_{1} = 2, w_{2} = 12

Show Solution