Solve y^2-(21-y)2=441

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

y_{1} = - 23, y_{2} = 21

Evaluate

y^{2} - (21 - y) \times 2 = 441

Multiply the terms

y^{2} - 2 (21 - y) = 441

Expand the expression

More Steps

Evaluate

- 2 (21 - y)

Apply the distributive property

- 2 \times 21 - (- 2 y)

Multiply the numbers

- 42 - (- 2 y)

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

- 42 + 2 y

y^{2} - 42 + 2 y = 441

Move the expression to the left side

y^{2} - 483 + 2 y = 0

Factor the expression

More Steps

Evaluate

y^{2} - 483 + 2 y

Reorder the terms

y^{2} + 2 y - 483

Rewrite the expression

y^{2} + (23 - 21) y - 483

Calculate

y^{2} + 23 y - 21 y - 483

Rewrite the expression

y \times y + y \times 23 - 21 y - 21 \times 23

Factor out y from the expression

y (y + 23) - 21 y - 21 \times 23

Factor out - 21 from the expression

y (y + 23) - 21 (y + 23)

Factor out y + 23 from the expression

(y - 21) (y + 23)

(y - 21) (y + 23) = 0

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

y - 21 = 0 y + 23 = 0

Solve the equation for y

More Steps

Evaluate

y - 21 = 0

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

y = 0 + 21

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

y = 21

y = 21 y + 23 = 0

Solve the equation for y

More Steps

Evaluate

y + 23 = 0

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

y = 0 - 23

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

y = - 23

y = 21 y = - 23

Solution

y_{1} = - 23, y_{2} = 21

Show Solution

Solve the quadratic equation

Graph