So the quadratic formula and completing the square give the same answer so

\[ax^2 + bx + c \Rightarrow \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}\] Right?

So making a formula for completing the square should lead me to the quadratic formula

- \(ax^ + bx + c \Rightarrow x^2 + \frac {bx + c}{a}\)
- \(x^2 = \frac {bx}{a} + \frac {c}{a} \Rightarrow (x + \frac {b}{2a})^2 - \frac {b^2}{4a^2} + \frac {c}{a}\)
- \((x + \frac {b}{2a})^2 - \frac {b^2}{4a^2} + \frac {c}{a} \Rightarrow (x + \frac {b}{2a})^2 - \frac {b^2 + 4ac}{4a^2}\)

If we assume that \(ax^2 + bx + c = 0\) Then

- \((x + \frac {b}{2a})^2 = \frac {b^2 + 4ac}{4a^2}\)
- \(x + \frac {b}{2a} = \pm \sqrt {\frac {b^2 + 4ac}{4a^2}} \Rightarrow \frac {\pm \sqrt {b^2 + 4ac}}{\pm \sqrt {4a^2}}\)
- \(x + \frac {b}{2a} = \frac {\pm \sqrt {b^2 - 4ac}}{2a}\)

So this then leads to

\[x = \frac {-b \pm \sqrt {b^2 -4ac}}{2a}\]

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

There are no comments in this discussion.