Solve for x 7^2+x^2=(x+1)^2

$7^{2} + x^{2} = {(x + 1)}^{2}$

Step 1

Raise $7$ to the power of $2$ .

$49 + x^{2} = {(x + 1)}^{2}$

Step 2

Simplify ${(x + 1)}^{2}$ .

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$49 + x^{2} = (x + 1) (x + 1)$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$49 + x^{2} = x (x + 1) + 1 (x + 1)$

Apply the distributive property.

$49 + x^{2} = x \cdot x + x \cdot 1 + 1 (x + 1)$

Apply the distributive property.

$49 + x^{2} = x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$49 + x^{2} = x^{2} + x \cdot 1 + 1 x + 1 \cdot 1$

Multiply $x$ by $1$ .

$49 + x^{2} = x^{2} + x + 1 x + 1 \cdot 1$

Multiply $x$ by $1$ .

$49 + x^{2} = x^{2} + x + x + 1 \cdot 1$

Multiply $1$ by $1$ .

$49 + x^{2} = x^{2} + x + x + 1$

Add $x$ and $x$ .

$49 + x^{2} = x^{2} + 2 x + 1$

Step 3

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

$x^{2} + 2 x + 1 = 49 + x^{2}$

Step 4

Move all terms containing $x$ to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

$x^{2} + 2 x + 1 - x^{2} = 49$

Combine the opposite terms in $x^{2} + 2 x + 1 - x^{2}$ .

Subtract $x^{2}$ from $x^{2}$ .

$2 x + 1 + 0 = 49$

Add $2 x + 1$ and $0$ .

$2 x + 1 = 49$

Step 5

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

Subtract $1$ from both sides of the equation.

$2 x = 49 - 1$

Subtract $1$ from $49$ .

$2 x = 48$

Step 6

Divide each term in $2 x = 48$ by $2$ and simplify.

Divide each term in $2 x = 48$ by $2$ .

$\frac{2 x}{2} = \frac{48}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{48}{2}$

Divide $x$ by $1$ .

$x = \frac{48}{2}$

Simplify the right side.

Divide $48$ by $2$ .

$x = 24$

Solve for x 7^2+x^2=(x+1)^2

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