Answer:
To solve the given quadratic equation solve using completing the perfect square
The two zeros of quadratic equation [tex]x^2-8x=242[/tex] are [tex]x=\sqrt{258}+4,\:x=-\sqrt{258}+4[/tex]
Step-by-step explanation:
Given quadratic equation [tex]x^2-8x=242[/tex]
We have to choose the most appropriate strategy to solve the given quadratic equation [tex]x^2-8x=242[/tex].
The given quadratic equation [tex]x^2-8x=242[/tex]
Solve using completing the perfect square, [tex]\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2[/tex]
Solve for a ,
[tex]2ax=-8x[/tex] , we get a = -4
[tex]\mathrm{Add\:}a^2=\left(-4\right)^2\mathrm{\:to\:both\:sides}[/tex]
[tex]x^2-8x+\left(-4\right)^2=242+\left(-4\right)^2[/tex]
left side becomes a perfect square, we get,
[tex]\left(x-4\right)^2=258[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
[tex]x-4=\pm\sqrt{258}\\\\\mathrm{Solve\:}\:x-4=\sqrt{258}:\quad x=\sqrt{258}+4[/tex]
[tex]\mathrm{Solve\:}\:x-4=-\sqrt{258}:\quad x=-\sqrt{258}+4[/tex]
Thus, the two zeros of quadratic equation [tex]x^2-8x=242[/tex] are [tex]x=\sqrt{258}+4,\:x=-\sqrt{258}+4[/tex]
Answer:
The most appropriate strategy to solve x2−8x=242 is quadratic formula.
Step-by-step explanation:
The equation is
[tex]x^2-8x=242[/tex]
Subtract 242 from both the sides.
[tex]x^2-8x-242=0[/tex]
Use quadratic formula to solve the given equation.
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{8\pm \sqrt{(-8)^2-4(1)(-242)}}{2(1)}[/tex]
[tex]x=\frac{8\pm \sqrt{1032}}{2}[/tex]
[tex]x=\frac{8\pm 2\sqrt{258}}{2}[/tex]
[tex]x=\frac{2(4\pm \sqrt{258})}{2}[/tex]
[tex]x=4\pm \sqrt{258}[/tex]
Therefore the most appropriate strategy to solve x2−8x=242 is quadratic formula.
