Solve x(28-x)=147

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 7, x_{2} = 21

Evaluate

x (28 - x) = 147

Expand the expression

More Steps

Evaluate

x (28 - x)

Apply the distributive property

x \times 28 - x \times x

Use the commutative property to reorder the terms

28 x - x \times x

Multiply the terms

28 x - x^{2}

28 x - x^{2} = 147

Move the expression to the left side

28 x - x^{2} - 147 = 0

Factor the expression

More Steps

Evaluate

28 x - x^{2} - 147

Reorder the terms

- x^{2} + 28 x - 147

Rewrite the expression

- x^{2} + (7 + 21) x - 147

Calculate

- x^{2} + 7 x + 21 x - 147

Rewrite the expression

- x \times x + x \times 7 + 21 x - 21 \times 7

Factor out - x from the expression

- x (x - 7) + 21 x - 21 \times 7

Factor out 21 from the expression

- x (x - 7) + 21 (x - 7)

Factor out x - 7 from the expression

(- x + 21) (x - 7)

(- x + 21) (x - 7) = 0

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

- x + 21 = 0 x - 7 = 0

Solve the equation for x

More Steps

Evaluate

- x + 21 = 0

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

- x = 0 - 21

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

- x = - 21

Change the signs on both sides of the equation

x = 21

x = 21 x - 7 = 0

Solve the equation for x

More Steps

Evaluate

x - 7 = 0

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

x = 0 + 7

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

x = 7

x = 21 x = 7

Solution

x_{1} = 7, x_{2} = 21

Show Solution