Solve 2(1-y^2)=5y-1

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

y_{1} = - 3, y_{2} = \frac{1}{2}

Alternative Form

y_{1} = - 3, y_{2} = 0.5

Evaluate

2 (1 - y^{2}) = 5 y - 1

Expand the expression

More Steps

Evaluate

2 (1 - y^{2})

Apply the distributive property

2 \times 1 - 2 y^{2}

Any expression multiplied by 1 remains the same

2 - 2 y^{2}

2 - 2 y^{2} = 5 y - 1

Move the expression to the left side

3 - 2 y^{2} - 5 y = 0

Factor the expression

More Steps

Evaluate

3 - 2 y^{2} - 5 y

Reorder the terms

3 - 5 y - 2 y^{2}

Rewrite the expression

3 + (- 6 + 1) y - 2 y^{2}

Calculate

3 - 6 y + y - 2 y^{2}

Rewrite the expression

3 - 3 \times 2 y + y - y \times 2 y

Factor out 3 from the expression

3 (1 - 2 y) + y - y \times 2 y

Factor out y from the expression

3 (1 - 2 y) + y (1 - 2 y)

Factor out 1 - 2 y from the expression

(3 + y) (1 - 2 y)

(3 + y) (1 - 2 y) = 0

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

1 - 2 y = 0 3 + y = 0

Solve the equation for y

More Steps

Evaluate

1 - 2 y = 0

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

- 2 y = 0 - 1

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

- 2 y = - 1

Change the signs on both sides of the equation

2 y = 1

Divide both sides

\frac{2 y}{2} = \frac{1}{2}

Divide the numbers

y = \frac{1}{2}

y = \frac{1}{2} 3 + y = 0

Solve the equation for y

More Steps

Evaluate

3 + y = 0

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

y = 0 - 3

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

y = - 3

y = \frac{1}{2} y = - 3

Solution

y_{1} = - 3, y_{2} = \frac{1}{2}

Alternative Form

y_{1} = - 3, y_{2} = 0.5

Show Solution