Answer:
Full explanation is down here
Step-by-step explanation:
Hello!
Recall the standard form of a quadratic: [tex]ax^2 + bx + c[/tex]
Solve for x:
[tex]ax^2 + bx + c = 0[/tex]
[tex]ax^2 + bx = -c[/tex]
[tex]x^2 + \frac{b}{a}x = \frac{-c}{a}[/tex]
[tex]x^2 + \frac{b}{a}x + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]
[tex](x+\frac{b}{2a})^2 = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]
[tex](x+\frac{b}{2a})^2 = \frac{-4ac+b^2}{4a^2}[/tex]
[tex]\sqrt{(x+\frac{b}{2a})^2} = \sqrt{\frac{-4ac+b^2}{4a^2}}[/tex]
[tex]x+\frac{b}{2a} = \frac{\pm\sqrt{-4ac+b^2}}{2a}[/tex]
[tex]x = \frac{\pm\sqrt{-4ac+b^2}}{2a} - \frac{b}{2a}[/tex]
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Completing the square:
Recall the standard form of a quadratic: [tex]ax^2 + bx + c[/tex]
To complete a square, we must find the "c" value given [tex]ax^2 + bx + c[/tex] so that it converts into a perfect square trinomial.
To find c:
Example: Given the expression [tex]x^2 - 8x[/tex], complete the square
Let's find the missing "c" value:
Now, complete the square:
To quickly factor this into a perfect square trinomial, simply take the value you get from the second step (Divide by 2) and plug it in.
Your factored expression will be (x - 4)²
