Solve 4x^2 = (x-12)^2

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 12, x_{2} = 4

Evaluate

4 x^{2} = (x - 12)^{2}

Expand the expression

More Steps

Evaluate

(x - 12)^{2}

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

x^{2} - 2 x \times 12 + 1 2^{2}

Calculate

x^{2} - 24 x + 144

4 x^{2} = x^{2} - 24 x + 144

Move the expression to the left side

3 x^{2} + 24 x - 144 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} + 24 x - 144

Rewrite the expression

3 x^{2} + 3 \times 8 x - 3 \times 48

Factor out 3 from the expression

3 (x^{2} + 8 x - 48)

Factor the expression

More Steps

Evaluate

x^{2} + 8 x - 48

Rewrite the expression

x^{2} + (12 - 4) x - 48

Calculate

x^{2} + 12 x - 4 x - 48

Rewrite the expression

x \times x + x \times 12 - 4 x - 4 \times 12

Factor out x from the expression

x (x + 12) - 4 x - 4 \times 12

Factor out - 4 from the expression

x (x + 12) - 4 (x + 12)

Factor out x + 12 from the expression

(x - 4) (x + 12)

3 (x - 4) (x + 12)

3 (x - 4) (x + 12) = 0

Divide the terms

(x - 4) (x + 12) = 0

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

x - 4 = 0 x + 12 = 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 = 4 x + 12 = 0

Solve the equation for x

More Steps

Evaluate

x + 12 = 0

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

x = 0 - 12

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

x = - 12

x = 4 x = - 12

Solution

x_{1} = - 12, x_{2} = 4

Show Solution