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

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 4, x_{2} = - 2

Evaluate

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

Expand the expression

More Steps

Evaluate

3 (x + 2)^{2}

Expand the expression

More Steps

Evaluate

(x + 2)^{2}

Use (a + b)^{2} = a^{2} + 2 ab + b^{2} to expand the expression

x^{2} + 2 x \times 2 + 2^{2}

Calculate

x^{2} + 4 x + 4

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

Apply the distributive property

3 x^{2} + 3 \times 4 x + 3 \times 4

Multiply the numbers

3 x^{2} + 12 x + 3 \times 4

Multiply the numbers

3 x^{2} + 12 x + 12

3 x^{2} + 12 x + 12 = x^{2} - 4

Move the expression to the left side

2 x^{2} + 12 x + 16 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + 12 x + 16

Rewrite the expression

2 x^{2} + 2 \times 6 x + 2 \times 8

Factor out 2 from the expression

2 (x^{2} + 6 x + 8)

Factor the expression

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Evaluate

x^{2} + 6 x + 8

Rewrite the expression

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

Calculate

x^{2} + 4 x + 2 x + 8

Rewrite the expression

x \times x + x \times 4 + 2 x + 2 \times 4

Factor out x from the expression

x (x + 4) + 2 x + 2 \times 4

Factor out 2 from the expression

x (x + 4) + 2 (x + 4)

Factor out x + 4 from the expression

(x + 2) (x + 4)

2 (x + 2) (x + 4)

2 (x + 2) (x + 4) = 0

Divide the terms

(x + 2) (x + 4) = 0

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

x + 2 = 0 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = - 2 x + 4 = 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 = - 2 x = - 4

Solution

x_{1} = - 4, x_{2} = - 2

Show Solution