Respuesta :
Value of q is [tex]\frac{105}{8}[/tex] .
Step-by-step explanation:
We have , the equation [tex]-2x^2+3=-9x[/tex] is rewritten in the form of [tex]-2(x-p)^2 +q=0[/tex] . We need to find What is the value of q . Let's find out:
Let's simplify equation [tex]-2x^2+3=-9x[/tex] into [tex]-2(x-p)^2 +q=0[/tex] :
⇒ [tex]-2x^2+3=-9x[/tex]
⇒ [tex]-2x^2+9x+3=0[/tex]
⇒ [tex]2x^2-9x=3[/tex]
⇒ [tex]2(x^2-\frac{9}{2}x)=3[/tex]
⇒ [tex](x^2-\frac{9}{2}x)=\frac{3}{2}[/tex]
⇒ [tex](x^2-2(1)\frac{9}{4}x)=\frac{3}{2}[/tex]
⇒ [tex](x^2-2(1)\frac{9}{4}x) + (\frac{9}{4})^2=\frac{3}{2} + (\frac{9}{4})^2[/tex]
⇒ [tex](x-\frac{9}{4})^2=\frac{3}{2} + (\frac{81}{16})[/tex]
⇒ [tex](x-\frac{9}{4})^2=\frac{24}{16} + (\frac{81}{16})[/tex]
⇒ [tex](x-\frac{9}{4})^2=\frac{105}{16}[/tex]
⇒ [tex]-2(x-\frac{9}{4})^2=-2(\frac{105}{16})[/tex]
⇒ [tex]-2(x-\frac{9}{4})^2=-\frac{105}{8}[/tex]
⇒ [tex]-2(x-\frac{9}{4})^2+\frac{105}{8} = 0[/tex]
Comparing this equation to [tex]-2(x-p)^2 +q=0[/tex] , [tex]q =\frac{105}{8}[/tex] .
Therefore ,Value of q is [tex]\frac{105}{8}[/tex] .
