Solve (x+4)^2 - 4(x+4)+3 = 0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 3, x_{2} = - 1

Evaluate

(x + 4)^{2} - 4 (x + 4) + 3 = 0

Subtract the terms

More Steps

Add the terms

(x + 4)^{2} - 4 (x + 4)

Expand the expression

x^{2} + 8 x + 16 - 4 (x + 4)

Rewrite the expression

(x + 4) (x + 4) - 4 (x + 4)

Factor the expression

(x + 4 - 4) (x + 4)

Since two opposites add up to 0,remove them form the expression

x (x + 4)

x (x + 4) + 3 = 0

Expand the expression

More Steps

Evaluate

x (x + 4)

Apply the distributive property

x \times x + x \times 4

Multiply the terms

x^{2} + x \times 4

Use the commutative property to reorder the terms

x^{2} + 4 x

x^{2} + 4 x + 3 = 0

Factor the expression

More Steps

Evaluate

x^{2} + 4 x + 3

Rewrite the expression

x^{2} + (3 + 1) x + 3

Calculate

x^{2} + 3 x + x + 3

Rewrite the expression

x \times x + x \times 3 + x + 3

Factor out x from the expression

x (x + 3) + x + 3

Factor out x + 3 from the expression

(x + 1) (x + 3)

(x + 1) (x + 3) = 0

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

x + 1 = 0 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = - 1 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x + 3 = 0

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

x = 0 - 3

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

x = - 3

x = - 1 x = - 3

Solution

x_{1} = - 3, x_{2} = - 1

Show Solution