Algebra Examples

$\frac{1}{2} (y + 4) = {(x - 7)}^{2}$

Step 1

Solve for $y$ .

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Step 1.1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} (y + 4)) = 2 {(x - 7)}^{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $2 (\frac{1}{2} (y + 4))$ .

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Step 1.2.1.1

Apply the distributive property.

$2 (\frac{1}{2} y + \frac{1}{2} \cdot 4) = 2 {(x - 7)}^{2}$

Step 1.2.1.2

Combine $\frac{1}{2}$ and $y$ .

$2 (\frac{y}{2} + \frac{1}{2} \cdot 4) = 2 {(x - 7)}^{2}$

Step 1.2.1.3

Cancel the common factor of $2$ .

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Step 1.2.1.3.1

Factor $2$ out of $4$ .

$2 (\frac{y}{2} + \frac{1}{2} \cdot (2 (2))) = 2 {(x - 7)}^{2}$

Step 1.2.1.3.2

Cancel the common factor.

$2 (\frac{y}{2} + \frac{1}{2} \cdot (2 \cdot 2)) = 2 {(x - 7)}^{2}$

Step 1.2.1.3.3

Rewrite the expression.

$2 (\frac{y}{2} + 2) = 2 {(x - 7)}^{2}$

Step 1.2.1.4

Apply the distributive property.

$2 \frac{y}{2} + 2 \cdot 2 = 2 {(x - 7)}^{2}$

Step 1.2.1.5

Cancel the common factor of $2$ .

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Step 1.2.1.5.1

Cancel the common factor.

$2 \frac{y}{2} + 2 \cdot 2 = 2 {(x - 7)}^{2}$

Step 1.2.1.5.2

Rewrite the expression.

$y + 2 \cdot 2 = 2 {(x - 7)}^{2}$

Step 1.2.1.6

Multiply $2$ by $2$ .

$y + 4 = 2 {(x - 7)}^{2}$

Step 1.3

Simplify $2 {(x - 7)}^{2}$ .

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Step 1.3.1

Rewrite.

$y + 4 = 0 + 0 + 2 {(x - 7)}^{2}$

Step 1.3.2

Rewrite ${(x - 7)}^{2}$ as $(x - 7) (x - 7)$ .

$y + 4 = 2 ((x - 7) (x - 7))$

Step 1.3.3

Expand $(x - 7) (x - 7)$ using the FOIL Method.

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Step 1.3.3.1

Apply the distributive property.

$y + 4 = 2 (x (x - 7) - 7 (x - 7))$

Step 1.3.3.2

Apply the distributive property.

$y + 4 = 2 (x \cdot x + x \cdot - 7 - 7 (x - 7))$

Step 1.3.3.3

Apply the distributive property.

$y + 4 = 2 (x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7)$

Step 1.3.4

Simplify and combine like terms.

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Step 1.3.4.1

Simplify each term.

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Step 1.3.4.1.1

Multiply $x$ by $x$ .

$y + 4 = 2 (x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7)$

Step 1.3.4.1.2

Move $- 7$ to the left of $x$ .

$y + 4 = 2 (x^{2} - 7 \cdot x - 7 x - 7 \cdot - 7)$

Step 1.3.4.1.3

Multiply $- 7$ by $- 7$ .

$y + 4 = 2 (x^{2} - 7 x - 7 x + 49)$

Step 1.3.4.2

Subtract $7 x$ from $- 7 x$ .

$y + 4 = 2 (x^{2} - 14 x + 49)$

Step 1.3.5

Apply the distributive property.

$y + 4 = 2 x^{2} + 2 (- 14 x) + 2 \cdot 49$

Step 1.3.6

Simplify.

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Step 1.3.6.1

Multiply $- 14$ by $2$ .

$y + 4 = 2 x^{2} - 28 x + 2 \cdot 49$

Step 1.3.6.2

Multiply $2$ by $49$ .

$y + 4 = 2 x^{2} - 28 x + 98$

Step 1.4

Move all terms not containing $y$ to the right side of the equation.

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Step 1.4.1

Subtract $4$ from both sides of the equation.

$y = 2 x^{2} - 28 x + 98 - 4$

Step 1.4.2

Subtract $4$ from $98$ .

$y = 2 x^{2} - 28 x + 94$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 3

The standard form is $2 x^{2} - 28 x + 94$ .

$y = 2 x^{2} - 28 x + 94$

Step 4