Question

Which of the following is a solution of X^2 - 7X = -5

Answer 1

The solution is:

`x=(√(29)+7)/(2),\:x=(-√(29)+7)/(2)`

Explanation:

Given the equation

`x^2\:-7x=\:-5`

`\mathrm{Add\:}a^2=\left(-(7)/(2)\right)^2\mathrm{\:to\:both\:sides}`

`x^2-7x+\left(-(7)/(2)\right)^2=-5+\left(-(7)/(2)\right)^2`

`x^2-7x+\left(-(7)/(2)\right)^2=(29)/(4)`

Apply perfect square rule

`\left(x-(7)/(2)\right)^2=(29)/(4)`

`\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=√(a),\:-√(a)`

solving

`x-(7)/(2)=\sqrt{(29)/(4)}`

`x-(7)/(2)=(√(29))/(√(4))`

`x-(7)/(2)=(√(29))/(2)`

`\mathrm{Add\:}(7)/(2)\mathrm{\:to\:both\:sides}`

`x-(7)/(2)+(7)/(2)=(√(29))/(2)+(7)/(2)`

`x=(√(29)+7)/(2)`

also solving

`x-(7)/(2)=-\sqrt{(29)/(4)}`

`\mathrm{Add\:}(7)/(2)\mathrm{\:to\:both\:sides}`

`x-(7)/(2)+(7)/(2)=-(√(29))/(2)+(7)/(2)`

`x=(-√(29)+7)/(2)`

Thus, the solution is:

`x=(√(29)+7)/(2),\:x=(-√(29)+7)/(2)`