Which are the solutions of x2 = –5x + 8?

  x = -2.5 ± √14.25

Step-by-step explanation:

Add 5x to prepare for "completing the square."

  x² +5x = 8

Add the square of half the x-coefficient:

  x² +5x + 2.5² = 8 + 2.5²

  (x +2.5)² = 14.25

Take the square root.

  x +2.5 = ±√14.25

Subtract 2.5.

  x = -2.5 ± √14.25 ≈ {-6.27492, 1.27592}

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1