How to solve (x)^(2)+px+9=0

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x)^(2)+px+9=0 | Equatix

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Question

$${ x }^{ 2 } +px+9=0$$

Solve for p

$p=-x-\frac{9}{x}$
$x\neq 0$

Steps for Solving Linear Equation

Subtract $x^{2}$ from both sides. Anything subtracted from zero gives its negation.

$$px+9=-x^{2}$$

Subtract $9$ from both sides.

$$px=-x^{2}-9$$

The equation is in standard form.

$$xp=-x^{2}-9$$

Divide both sides by $x$.

$$\frac{xp}{x}=\frac{-x^{2}-9}{x}$$

Dividing by $x$ undoes the multiplication by $x$.

$$p=\frac{-x^{2}-9}{x}$$

Divide $-x^{2}-9$ by $x$.

$$p=-x-\frac{9}{x}$$

Show Solution

Solve for x (complex solution)

$x=\frac{\sqrt{p^{2}-36}-p}{2}$
$x=\frac{-\sqrt{p^{2}-36}-p}{2}$

Solve for x

$x=\frac{\sqrt{p^{2}-36}-p}{2}$
$x=\frac{-\sqrt{p^{2}-36}-p}{2}\text{, }|p|\geq 6$