Answer:
We have quadratic equation, ax² + bx + c = 0
[tex]x^2+\frac{b}{a} x+\frac{c}{a} =0\\ \\ x^2+\frac{b}{a} x=-\frac{c}{a}[/tex]
Adding both sides with square of half of b/a.
[tex]x^2+\frac{b}{a} x+(\frac{b}{2a})^2= -\frac{c}{a}+(\frac{b}{2a})^2\\ \\ (x+\frac{b}{2a})^2= -\frac{c}{a}+\frac{b^2}{4a^2}\\ \\ (x+\frac{b}{2a})^2= -\frac{4ac}{4a^2}+\frac{b^2}{4a^2}\\ \\ (x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}[/tex]
[tex]x+\frac{b}{2a}=[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x = -\frac{b}{2a}[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
These are the steps Florence should do next.
The solution to ax² + bx + c = 0 is [tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]
A quadratic function is an equation of degree 2.
Given the equation:
ax² + bx + c = 0
Subtracting c from both sides to get:
ax² + bx = -c
Dividing through by a:
x² + (b/a)x = -c/a
Add to both sides the square of half of the coefficient of x that is (b²/4a):
x² + (b/a)x + (b²/4a)= -c/a + (b²/4a)
(x + b/2a)² = (b²-4c/4a)
[tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]
The solution to ax² + bx + c = 0 is [tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]
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