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.

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Question

$$49 x ^ { 2 } + k x + 1 = 0$$

Solve for k

$k=-49x-\frac{1}{x}$
$x\neq 0$

Steps for Solving Linear Equation

Subtract $49x^{2}$ from both sides. Anything subtracted from zero gives its negation.

$$kx+1=-49x^{2}$$

Subtract $1$ from both sides.

$$kx=-49x^{2}-1$$

The equation is in standard form.

$$xk=-49x^{2}-1$$

Divide both sides by $x$.

$$\frac{xk}{x}=\frac{-49x^{2}-1}{x}$$

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

$$k=\frac{-49x^{2}-1}{x}$$

Divide $-49x^{2}-1$ by $x$.

$$k=-49x-\frac{1}{x}$$

Show Solution

Solve for x (complex solution)

$x=\frac{\sqrt{k^{2}-196}-k}{98}$
$x=\frac{-\sqrt{k^{2}-196}-k}{98}$

Solve for x

$x=\frac{\sqrt{k^{2}-196}-k}{98}$
$x=\frac{-\sqrt{k^{2}-196}-k}{98}\text{, }|k|\geq 14$