Question

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

Answer 1

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.

Answer 2

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`