Solve 2y^2-11y-261

Question

Factor the expression

(y + 9) (2 y - 29)

Evaluate

2 y^{2} - 11 y - 261

Rewrite the expression

2 y^{2} + (- 29 + 18) y - 261

Calculate

2 y^{2} - 29 y + 18 y - 261

Rewrite the expression

y \times 2 y - y \times 29 + 9 \times 2 y - 9 \times 29

Factor out y from the expression

y (2 y - 29) + 9 \times 2 y - 9 \times 29

Factor out 9 from the expression

y (2 y - 29) + 9 (2 y - 29)

Solution

(y + 9) (2 y - 29)

Show Solution

y_{1} = - 9, y_{2} = \frac{29}{2}

Alternative Form

y_{1} = - 9, y_{2} = 14.5

Evaluate

2 y^{2} - 11 y - 261

To find the roots of the expression,set the expression equal to 0

2 y^{2} - 11 y - 261 = 0

Factor the expression

More Steps

Evaluate

2 y^{2} - 11 y - 261

Rewrite the expression

2 y^{2} + (- 29 + 18) y - 261

Calculate

2 y^{2} - 29 y + 18 y - 261

Rewrite the expression

y \times 2 y - y \times 29 + 9 \times 2 y - 9 \times 29

Factor out y from the expression

y (2 y - 29) + 9 \times 2 y - 9 \times 29

Factor out 9 from the expression

y (2 y - 29) + 9 (2 y - 29)

Factor out 2 y - 29 from the expression

(y + 9) (2 y - 29)

(y + 9) (2 y - 29) = 0

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

y + 9 = 0 2 y - 29 = 0

Solve the equation for y

More Steps

Evaluate

y + 9 = 0

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

y = 0 - 9

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

y = - 9

y = - 9 2 y - 29 = 0

Solve the equation for y

More Steps

Evaluate

2 y - 29 = 0

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

2 y = 0 + 29

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

2 y = 29

Divide both sides

\frac{2 y}{2} = \frac{29}{2}

Divide the numbers

y = \frac{29}{2}

y = - 9 y = \frac{29}{2}

Solution

y_{1} = - 9, y_{2} = \frac{29}{2}

Alternative Form

y_{1} = - 9, y_{2} = 14.5

Show Solution