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

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

Step 1

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $7$ by $7$ .

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

Add $7 x$ and $7 x$ .

${(x - 7)}^{2} + x^{2} = x^{2} + 14 x + 49$

Step 2

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

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

${(x - 7)}^{2} + x^{2} - x^{2} = 14 x + 49$

Subtract $14 x$ from both sides of the equation.

${(x - 7)}^{2} + x^{2} - x^{2} - 14 x = 49$

Combine the opposite terms in ${(x - 7)}^{2} + x^{2} - x^{2} - 14 x$ .

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

${(x - 7)}^{2} + 0 - 14 x = 49$

Add ${(x - 7)}^{2}$ and $0$ .

${(x - 7)}^{2} - 14 x = 49$

Simplify each term.

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

$(x - 7) (x - 7) - 14 x = 49$

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

Apply the distributive property.

$x (x - 7) - 7 (x - 7) - 14 x = 49$

Apply the distributive property.

$x \cdot x + x \cdot - 7 - 7 (x - 7) - 14 x = 49$

Apply the distributive property.

$x \cdot x + x \cdot - 7 - 7 x - 7 \cdot - 7 - 14 x = 49$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 7 - 7 x - 7 \cdot - 7 - 14 x = 49$

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

$x^{2} - 7 \cdot x - 7 x - 7 \cdot - 7 - 14 x = 49$

Multiply $- 7$ by $- 7$ .

$x^{2} - 7 x - 7 x + 49 - 14 x = 49$

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

$x^{2} - 14 x + 49 - 14 x = 49$

Subtract $14 x$ from $- 14 x$ .

$x^{2} - 28 x + 49 = 49$

Step 3

Subtract $49$ from both sides of the equation.

$x^{2} - 28 x + 49 - 49 = 0$

Step 4

Combine the opposite terms in $x^{2} - 28 x + 49 - 49$ .

Subtract $49$ from $49$ .

$x^{2} - 28 x + 0 = 0$

Add $x^{2} - 28 x$ and $0$ .

$x^{2} - 28 x = 0$

Step 5

Factor $x$ out of $x^{2} - 28 x$ .

Factor $x$ out of $x^{2}$ .

$x \cdot x - 28 x = 0$

Factor $x$ out of $- 28 x$ .

$x \cdot x + x \cdot - 28 = 0$

Factor $x$ out of $x \cdot x + x \cdot - 28$ .

$x (x - 28) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 28 = 0$

Step 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

Set $x - 28$ equal to $0$ and solve for $x$ .

Set $x - 28$ equal to $0$ .

$x - 28 = 0$

Add $28$ to both sides of the equation.

$x = 28$

Step 9

The final solution is all the values that make $x (x - 28) = 0$ true.

$x = 0, 28$

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

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