Question

Consider the equation: 12x=13-x^212x=13−x 2 12, x, equals, 13, minus, x, squared 1) Rewrite the equation by completing the square. Your equation should look like (x+c)^2=d(x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation

Answer 1

(x+6)^2=49 and x=−6±7

Explanation:

Answer 2

`(x + 6)^2 = 49`

`x = 1` or
`x = -13`

Explanation:

Given

`12x = 13 - x^2`

Using Completing the Square

`12x = 13 - x^2` ---- Add
`x^2` to both sides

`x^2 + 12x = 13 - x^2 + x^2`

`x^2 + 12x = 13`

Divide the coefficient of x by 2; then add the square to both sides

`x^2 + 12x + 6^2 = 13 + 6^2`

`x^2 + 12x + 36 = 13 + 36`

`x^2 + 12x + 36 = 49`

Factorize

`x^2 + 6x + 6x + 36 = 49`

`x(x + 6) + 6(x + 6) = 49`

`(x + 6)(x + 6) = 49`

`(x + 6)^2 = 49`

Hence, the equation is
`(x + 6)^2 = 49`

Solving further

Take square root of both sides

`(x + 6) = √(49)`

`x + 6 = \±7`

`x = \±7- 6`

This implies that

`x = 7 - 6` or
`x = -7 -6`

`x = 1` or
`x = -13`

HEnce, the solutions are
`x = 1` or
`x = -13`