Question

Solve with Quadratics

Answer 1

x = 1 ±
`√(6)`

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 = ±
`√(6)` ( add 1 to both sides )

x = 1 ±
`√(6)` ← exact solutions

Answer 2

`x \pm\sqrt6 +1`

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
• 
  `√((x-1)^2) = √(6)`
• x - 1 = ±√6
• x = ±√6 + 1

The solutions are
`x \pm\sqrt6 +1`