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Which strategy is the most appropriate strategy to solve x2−8x=242

2 Answers

1 vote

Answer:

The most appropriate strategy to solve x2−8x=242 is quadratic formula.

Explanation:

The equation is


x^2-8x=242

Subtract 242 from both the sides.


x^2-8x-242=0

Use quadratic formula to solve the given equation.


x=(-b\pm √(b^2-4ac))/(2a)


x=(8\pm √((-8)^2-4(1)(-242)))/(2(1))


x=(8\pm √(1032))/(2)


x=(8\pm 2√(258))/(2)


x=(2(4\pm √(258)))/(2)


x=4\pm √(258)

Therefore the most appropriate strategy to solve x2−8x=242 is quadratic formula.

User Derek Corcoran
by
6.8k points
6 votes

Answer:

To solve the given quadratic equation solve using completing the perfect square

The two zeros of quadratic equation
x^2-8x=242 are
x=√(258)+4,\:x=-√(258)+4

Explanation:

Given quadratic equation
x^2-8x=242

We have to choose the most appropriate strategy to solve the given quadratic equation
x^2-8x=242.

The given quadratic equation
x^2-8x=242

Solve using completing the perfect square,
\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2

Solve for a ,


2ax=-8x , we get a = -4


\mathrm{Add\:}a^2=\left(-4\right)^2\mathrm{\:to\:both\:sides}


x^2-8x+\left(-4\right)^2=242+\left(-4\right)^2

left side becomes a perfect square, we get,


\left(x-4\right)^2=258


\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=√(a),\:-√(a)


x-4=\pm√(258)\\\\\mathrm{Solve\:}\:x-4=√(258):\quad x=√(258)+4


\mathrm{Solve\:}\:x-4=-√(258):\quad x=-√(258)+4

Thus, the two zeros of quadratic equation
x^2-8x=242 are
x=√(258)+4,\:x=-√(258)+4

User Himal Acharya
by
7.5k points