Question

Khan Academy please show work​

Answer 1

Rewriting the equation in the form (x+c)²=d by completing the square

• 
  `\left(x+5\right)^2=16`

The solutions to the quadratic equation are:

• 
  `x=-1,\:x=-9`

Explanation:

Given the equation

`x^2+10x+22=13`

subtract 22 from both sides

`x^2+10x+22-22=13-22`

simplify

`x^2+10x=-9`

Rewriting the equation in the form (x+c)²=d by completing the square

`x^2+10x+5^2=-9+5^2`

`x^2+10x+5^2=16`

`\left(x+5\right)^2=16`

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

solve

`x+5=√(16)`

`x+5=√(4^2)`

`x+5=4`

`x=-1`

also solving

`x+5=-√(16)`

`x+5=-4`

`x=-9`

Therefore, the solutions to the quadratic equation are:

`x=-1,\:x=-9`