Answer:
x = 8, or -11.
Step-by-step explanation:
Given:
the given expression.
[tex]2x^2+6x-14=0[/tex]
We need to solve the given expression by completing the square.
Solution:
Rewrite the expression as:
[tex]2x^2+6x-14=0[/tex]
Whole expression divided by 2.
[tex]x^2+3x-7=0[/tex]
Where:
[tex]b=3\ and\ c=-7[/tex]
Solve the given expression by the following formula.
[tex]x^2+bx+c=(x+\frac{b}{2})^2-(\frac{b}{2})^2+c=0[/tex] --------------(1)
Substitute b and c value in equation 1.
[tex](x+\frac{3}{2})^2-(\frac{3}{2})+(-7)=0[/tex]
[tex](x+\frac{3}{2})^2-\frac{3}{2}-7=0[/tex]
[tex](x+\frac{3}{2})^2+\frac{-3-7\times 2}{2}=0[/tex]
[tex](x+\frac{3}{2})^2+\frac{-3-14}{2}=0[/tex]
[tex](x+\frac{3}{2})^2+\frac{-19}{2}=0[/tex]
[tex](x+\frac{3}{2})^2-\frac{19}{2}=0[/tex]
Add [tex]\frac{19}{2}[/tex] both side of the equation.
[tex](x+\frac{3}{2})^2-\frac{19}{2}+\frac{19}{2}=\frac{19}{2}[/tex]
[tex](x+\frac{3}{2})^2=\frac{19}{2}[/tex]
Square root of the whole equation.
[tex]\sqrt{(x+\frac{3}{2})^2}=\sqrt{\frac{19}{2}}[/tex]
[tex]x+\frac{3}{2}=\pm\frac{19}{2}[/tex] --------(1)
For positive sign.
Add [tex]\frac{3}{2}[/tex] both side of the equation 1.
[tex]x+\frac{3}{2}-\frac{3}{2}=\frac{19}{2}-\frac{3}{2}[/tex]
[tex]x=\frac{19}{2}-\frac{3}{2}[/tex]
[tex]x=\frac{19-3}{2}[/tex]
[tex]x=\frac{16}{2}[/tex]
x = 8
Similarly for negative sign.
x = -11
Therefore, the value of x = 8, or -11.
