Solve for x x^2+(7-x)^2=25

$x^{2} + {(7 - x)}^{2} = 25$

Step 1

Subtract $25$ from both sides of the equation.

$x^{2} + {(7 - x)}^{2} - 25 = 0$

Step 2

Simplify $x^{2} + {(7 - x)}^{2} - 25$ .

Simplify each term.

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

$x^{2} + (7 - x) (7 - x) - 25 = 0$

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

Apply the distributive property.

$x^{2} + 7 (7 - x) - x (7 - x) - 25 = 0$

Apply the distributive property.

$x^{2} + 7 \cdot 7 + 7 (- x) - x (7 - x) - 25 = 0$

Apply the distributive property.

$x^{2} + 7 \cdot 7 + 7 (- x) - x \cdot 7 - x (- x) - 25 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $7$ .

$x^{2} + 49 + 7 (- x) - x \cdot 7 - x (- x) - 25 = 0$

Multiply $- 1$ by $7$ .

$x^{2} + 49 - 7 x - x \cdot 7 - x (- x) - 25 = 0$

Multiply $7$ by $- 1$ .

$x^{2} + 49 - 7 x - 7 x - x (- x) - 25 = 0$

Rewrite using the commutative property of multiplication.

$x^{2} + 49 - 7 x - 7 x - 1 \cdot - 1 x \cdot x - 25 = 0$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{2} + 49 - 7 x - 7 x - 1 \cdot - 1 (x \cdot x) - 25 = 0$

Multiply $x$ by $x$ .

$x^{2} + 49 - 7 x - 7 x - 1 \cdot - 1 x^{2} - 25 = 0$

Multiply $- 1$ by $- 1$ .

$x^{2} + 49 - 7 x - 7 x + 1 x^{2} - 25 = 0$

Multiply $x^{2}$ by $1$ .

$x^{2} + 49 - 7 x - 7 x + x^{2} - 25 = 0$

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

$x^{2} + 49 - 14 x + x^{2} - 25 = 0$

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} + 49 - 14 x - 25 = 0$

Subtract $25$ from $49$ .

$2 x^{2} - 14 x + 24 = 0$

Step 3

Factor the left side of the equation.

Factor $2$ out of $2 x^{2} - 14 x + 24$ .

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

$2 (x^{2}) - 14 x + 24 = 0$

Factor $2$ out of $- 14 x$ .

$2 (x^{2}) + 2 (- 7 x) + 24 = 0$

Factor $2$ out of $24$ .

$2 x^{2} + 2 (- 7 x) + 2 \cdot 12 = 0$

Factor $2$ out of $2 x^{2} + 2 (- 7 x)$ .

$2 (x^{2} - 7 x) + 2 \cdot 12 = 0$

Factor $2$ out of $2 (x^{2} - 7 x) + 2 \cdot 12$ .

$2 (x^{2} - 7 x + 12) = 0$

Factor.

Factor $x^{2} - 7 x + 12$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $12$ and whose sum is $- 7$ .

$- 4, - 3$

Write the factored form using these integers.

$2 ((x - 4) (x - 3)) = 0$

Remove unnecessary parentheses.

$2 (x - 4) (x - 3) = 0$

Step 4

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

$x - 4 = 0$

$x - 3 = 0$

Step 5

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Step 6

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Step 7

The final solution is all the values that make $2 (x - 4) (x - 3) = 0$ true.

$x = 4, 3$

Solve for x x^2+(7-x)^2=25

Related Questions

Support LCMGCF.com by disabling your adblocker.