Respuesta :

Answer:

x = 1 ± [tex]\sqrt{6}[/tex]

Step-by-step explanation:

Given

2x² - 4x = 10 ( divide through by 2 )

x² - 2x = 5

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 1)x + 1 = 5 + 1

(x - 1)² = 6 ( take the square root of both sides )

x - 1 = ± [tex]\sqrt{6}[/tex] ( add 1 to both sides )

x = 1 ± [tex]\sqrt{6}[/tex] ← exact solutions

chetankachana

Answer:

[tex]x \pm\sqrt6 +1[/tex]

Step-by-step explanation:

Hello!

Standard form of a quadratic: ax² + bx + c

Solve:

  • 2x² - 4x = 10
  • 2x² - 4x - 10 = 0
  • 2(x² - 2x - 5) = 0
  • x² - 2x - 5 = 0

Now, complete the square:

  • Take the b-value in our equation (-2)
  • Divide it by 2 (-1)
  • Square it (1)

Add and subtract that in our equation:

  • x² - 2x - 5 = 0
  • x² - 2x + 1 - 5 - 1 = 0

Factor the perfect square trinomial:

  • (x - 1)² - 6 = 0
  • (x - 1)² = 6
  • [tex]\sqrt{(x-1)^2} = \sqrt{6}[/tex]
  • x - 1 = ±√6
  • x = ±√6 + 1

The solutions are [tex]x \pm\sqrt6 +1[/tex]

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