Solve by Factoring 2x=3-x^2

$2 x = 3 - x^{2}$

Step 1

Move all the expressions to the left side of the equation.

Subtract $3$ from both sides of the equation.

$2 x - 3 = - x^{2}$

Add $x^{2}$ to both sides of the equation.

$2 x - 3 + x^{2} = 0$

Step 2

Factor $2 x - 3 + x^{2}$ 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 $- 3$ and whose sum is $2$ .

$- 1, 3$

Write the factored form using these integers.

$(x - 1) (x + 3) = 0$

Step 3

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

$x - 1 = 0$

$x + 3 = 0$

Step 4

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 5

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 6

The final solution is all the values that make $(x - 1) (x + 3) = 0$ true.

$x = 1, - 3$

Solve by Factoring 2x=3-x^2

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