Answer:
8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
Step-by-step explanation:
Solving Quadratic Equations
Sometimes it's preferred to solve quadratic equations without the use of the known quadratic formula solver. One of the most-used methods consists of completing squares and solving for x.
We have the equation
[tex]\displaystyle 8x^2+16x+3=0[/tex]
We separate variables from constants
[tex]\displaystyle 8x^2+16x=-3[/tex]
Taking the common factor 8
[tex]\displaystyle 8(x^2+2x)=-3[/tex]
Completing squares in the brackets and balancing the equation in the right side
[tex]\displaystyle 8(x^2+2x+1)=-3+8[/tex]
Factoring the perfect square
[tex]\displaystyle 8(x+1)^2=5[/tex]
Isolating x
[tex]\displaystyle (x+1)^2=\frac{5}{8}[/tex]
[tex]\displaystyle (x+1)=\pm \sqrt{\frac{5}{8}}[/tex]
[tex]\displaystyle x=-1\pm \sqrt{\frac{5}{8}}[/tex]
We can clearly see the steps used to solve the quadratic equation are (in order and written like in the question)
8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
