Which equation shows the quadratic formula used correctly to solve 5x2 + 3x – 4 = 0 for x?
5x^2+3x-4=0
x^2+3x/5-4/5=0
x^2+3x/5=4/5
x^2+3x/5+9/100=89/100
(x+3/10)^2=89/100
x+3/10=±(√89)/10
x=-3/10±√89/100
x=-3±(√89/10)
Answer:
The equation \(x=\frac{-3\pm \sqrt{(3)^2-4(5)(-4)}}{2(5)}\) shows the quadratic formula used correctly to solve the given quadratic equation.
Step-by-step explanation:
The given equation is
\(5x^2+3x-4=0\) .... (1)
If a quadratic equation is defined as
\(ax^2+bx+c=0\) ..... (2)
then the quadratic formula is
\(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)
From equation (1) and (2), we get
\(a=5,b=3,c=-4\)
Using quadratic formula we get
\(x=\frac{-3\pm \sqrt{(3)^2-4(5)(-4)}}{2(5)}\)
Therefore the equation \(x=\frac{-3\pm \sqrt{(3)^2-4(5)(-4)}}{2(5)}\) shows the quadratic formula used correctly to solve the given quadratic equation.