Solve x(34-x)=120

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 4, x_{2} = 30

Evaluate

x (34 - x) = 120

Expand the expression

More Steps

Evaluate

x (34 - x)

Apply the distributive property

x \times 34 - x \times x

Use the commutative property to reorder the terms

34 x - x \times x

Multiply the terms

34 x - x^{2}

34 x - x^{2} = 120

Move the expression to the left side

34 x - x^{2} - 120 = 0

Factor the expression

More Steps

Evaluate

34 x - x^{2} - 120

Reorder the terms

- x^{2} + 34 x - 120

Rewrite the expression

- x^{2} + (4 + 30) x - 120

Calculate

- x^{2} + 4 x + 30 x - 120

Rewrite the expression

- x \times x + x \times 4 + 30 x - 30 \times 4

Factor out - x from the expression

- x (x - 4) + 30 x - 30 \times 4

Factor out 30 from the expression

- x (x - 4) + 30 (x - 4)

Factor out x - 4 from the expression

(- x + 30) (x - 4)

(- x + 30) (x - 4) = 0

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

- x + 30 = 0 x - 4 = 0

Solve the equation for x

More Steps

Evaluate

- x + 30 = 0

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

- x = 0 - 30

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

- x = - 30

Change the signs on both sides of the equation

x = 30

x = 30 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 = 30 x = 4

Solution

x_{1} = 4, x_{2} = 30

Show Solution