Solve for x x=-x^2+30

$x = - x^{2} + 30$

Step 1

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

$x + x^{2} = 30$

Step 2

Subtract $30$ from both sides of the equation.

$x + x^{2} - 30 = 0$

Step 3

Factor the left side of the equation.

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$u + u^{2} - 30 = 0$

Factor $u + u^{2} - 30$ 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 $- 30$ and whose sum is $1$ .

$- 5, 6$

Write the factored form using these integers.

$(u - 5) (u + 6) = 0$

Replace all occurrences of $u$ with $x$ .

$(x - 5) (x + 6) = 0$

Step 4

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

$x - 5 = 0$

$x + 6 = 0$

Step 5

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Step 6

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 7

The final solution is all the values that make $(x - 5) (x + 6) = 0$ true.

$x = 5, - 6$

Solve for x x=-x^2+30

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