How to solve (x)^(2)-px+q=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+q=0 | Equatix

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Question

$${ x }^{ 2 } -px+q=0$$

Solve for p (complex solution)

$\left\{\begin{matrix}p=x+\frac{q}{x}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&q=0\text{ and }x=0\end{matrix}\right.$

Steps for Solving Linear Equation

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

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

Subtract $q$ from both sides.

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

The equation is in standard form.

$$\left(-x\right)p=-x^{2}-q$$

Divide both sides by $-x$.

$$\frac{\left(-x\right)p}{-x}=\frac{-x^{2}-q}{-x}$$

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

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

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

$$p=x+\frac{q}{x}$$

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Solve for p

$\left\{\begin{matrix}p=x+\frac{q}{x}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&q=0\text{ and }x=0\end{matrix}\right.$

Steps for Solving Linear Equation

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

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

Subtract $q$ from both sides.

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

The equation is in standard form.

$$\left(-x\right)p=-x^{2}-q$$

Divide both sides by $-x$.

$$\frac{\left(-x\right)p}{-x}=\frac{-x^{2}-q}{-x}$$

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

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

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

$$p=x+\frac{q}{x}$$

Show Solution

Solve for q

$q=-x\left(x-p\right)$

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Example

Question

Solve for p (complex solution)

Steps for Solving Linear Equation

Solve for p

Steps for Solving Linear Equation

Solve for q

Solution Steps