Answer:
[tex] {x}^{2} - 12x + 5 = 7[/tex]
i) move constants to the right-hand side and change its sign
[tex] {x}^{2} - 12 {x} = 7 - 5[/tex]
ii) subtract the numbers
[tex] {x}^{2} - 12x = 2[/tex]
iii) add (12/2)² to both sides of the equation
[tex] {x}^{2} - 12x + ( \frac{12}{2} ) {}^{2} = 2 + ( \frac{12}{2} ) {}^{2} [/tex]
iv) using a²-2ab+b²=(a-b)² , factorize the expression
[tex](x - \frac{12}{2} ) {}^{2} = 2 + ( \frac{12}{2} ) {}^{2} [/tex]
v) calculate the value
[tex](x - \frac{12}{2}) {}^{2} = 2 + 36[/tex]
[tex](x - \frac{12}{2}) {}^{2} = 38[/tex]
vi) reduce the fraction
[tex](x - 6) {}^{2} = 38[/tex]
vii) solve the equation for x
[tex]x - 6 = + - \sqrt{38} [/tex]
1) first value of x
[tex]x - 6 = \sqrt{38} [/tex]
[tex]x = \sqrt{38} + 6 \: or \: 12.16[/tex]
2) second value of x
[tex]x - 6 = - \sqrt{38} [/tex]
[tex]x = - \sqrt{38} + 6 \: or \: - 0.16[/tex]
