Algebra Examples

$f (x) = a x^{2} + b x + c$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$a x^{2} + b x + c = f (x)$

Step 2

Subtract $f (x)$ from both sides of the equation.

$a x^{2} + b x + c - f (x) = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = a$ , $b = b$ , and $c = c - f (x)$ into the quadratic formula and solve for $x$ .

$\frac{- b \pm \sqrt{b^{2} - 4 \cdot (a \cdot (c - f (x)))}}{2 a}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c - 4 a (- f (x))}}{2 a}$

Step 5.2

Multiply $- 1$ by $- 4$ .

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c + 4 a f (x)}}{2 a}$

Step 6

The final answer is the combination of both solutions.

$x = - \frac{b - \sqrt{b^{2} - 4 a c + 4 a f (x)}}{2 a}, - \frac{b + \sqrt{b^{2} - 4 a c + 4 a f (x)}}{2 a}$