Algebra Examples

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

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Add $5$ to both sides of the equation.

$2 {(x - 1)}^{2} = y + 5$

Divide each term in $2 {(x - 1)}^{2} = y + 5$ by $2$ and simplify.

Tap for more steps...

Divide each term in $2 {(x - 1)}^{2} = y + 5$ by $2$ .

$\frac{2 {(x - 1)}^{2}}{2} = \frac{y}{2} + \frac{5}{2}$

Simplify the left side.

Tap for more steps...

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\frac{2 {(x - 1)}^{2}}{2} = \frac{y}{2} + \frac{5}{2}$

Divide ${(x - 1)}^{2}$ by $1$ .

${(x - 1)}^{2} = \frac{y}{2} + \frac{5}{2}$

Factor.

Tap for more steps...

Combine the numerators over the common denominator.

${(x - 1)}^{2} = \frac{y + 5}{2}$

Reorder terms.

${(x - 1)}^{2} = \frac{1}{2} (y + 5)$