Solve for x f(x)=x^2-5x+3 , f(x)=-3

$f (x) = x^{2} - 5 x + 3$ , $f (x) = - 3$

Step 1

Substitute $- 3$ for $f (x)$ .

$- 3 = x^{2} - 5 x + 3$

Step 2

Solve for $x$ .

Rewrite the equation as $x^{2} - 5 x + 3 = - 3$ .

$x^{2} - 5 x + 3 = - 3$

Add $3$ to both sides of the equation.

$x^{2} - 5 x + 3 + 3 = 0$

Add $3$ and $3$ .

$x^{2} - 5 x + 6 = 0$

Factor $x^{2} - 5 x + 6$ 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 $6$ and whose sum is $- 5$ .

$- 3, - 2$

Write the factored form using these integers.

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

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

$x - 3 = 0$

$x - 2 = 0$

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.

$x = 3$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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

$x = 3, 2$

Solve for x f(x)=x^2-5x+3 , f(x)=-3

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