Solve (2x-4)(x-4) = 4800

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 46, x_{2} = 52

Evaluate

(2 x - 4) (x - 4) = 4800

Expand the expression

More Steps

Evaluate

(2 x - 4) (x - 4)

Apply the distributive property

2 x \times x - 2 x \times 4 - 4 x - (- 4 \times 4)

Multiply the terms

2 x^{2} - 2 x \times 4 - 4 x - (- 4 \times 4)

Multiply the numbers

2 x^{2} - 8 x - 4 x - (- 4 \times 4)

Multiply the numbers

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

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

Subtract the terms

More Steps

Evaluate

- 8 x - 4 x

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

(- 8 - 4) x

Subtract the numbers

- 12 x

2 x^{2} - 12 x + 16

2 x^{2} - 12 x + 16 = 4800

Move the expression to the left side

2 x^{2} - 12 x - 4784 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 12 x - 4784

Rewrite the expression

2 x^{2} - 2 \times 6 x - 2 \times 2392

Factor out 2 from the expression

2 (x^{2} - 6 x - 2392)

Factor the expression

More Steps

Evaluate

x^{2} - 6 x - 2392

Rewrite the expression

x^{2} + (46 - 52) x - 2392

Calculate

x^{2} + 46 x - 52 x - 2392

Rewrite the expression

x \times x + x \times 46 - 52 x - 52 \times 46

Factor out x from the expression

x (x + 46) - 52 x - 52 \times 46

Factor out - 52 from the expression

x (x + 46) - 52 (x + 46)

Factor out x + 46 from the expression

(x - 52) (x + 46)

2 (x - 52) (x + 46)

2 (x - 52) (x + 46) = 0

Divide the terms

(x - 52) (x + 46) = 0

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

x - 52 = 0 x + 46 = 0

Solve the equation for x

More Steps

Evaluate

x - 52 = 0

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

x = 0 + 52

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

x = 52

x = 52 x + 46 = 0

Solve the equation for x

More Steps

Evaluate

x + 46 = 0

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

x = 0 - 46

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

x = - 46

x = 52 x = - 46

Solution

x_{1} = - 46, x_{2} = 52

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