Question

Solve the following quadratic equation by completing the square: x^2-12x+5=7
PLS HELP ASAP

Answer 1

`{x}^(2) - 12x + 5 = 7`

i) move constants to the right-hand side and change its sign

`{x}^(2) - 12 {x} = 7 - 5`

ii) subtract the numbers

`{x}^(2) - 12x = 2`

iii) add (12/2)² to both sides of the equation

`{x}^(2) - 12x + ( (12)/(2) ) {}^(2) = 2 + ( (12)/(2) ) {}^(2)`

iv) using a²-2ab+b²=(a-b)² , factorize the expression

`(x - (12)/(2) ) {}^(2) = 2 + ( (12)/(2) ) {}^(2)`

v) calculate the value

`(x - (12)/(2)) {}^(2) = 2 + 36`

`(x - (12)/(2)) {}^(2) = 38`

vi) reduce the fraction

`(x - 6) {}^(2) = 38`

vii) solve the equation for x

`x - 6 = + - √(38)`

1) first value of x

`x - 6 = √(38)`

`x = √(38) + 6 \: or \: 12.16`

2) second value of x

`x - 6 = - √(38)`

`x = - √(38) + 6 \: or \: - 0.16`