Question

Khan Academy please show work​

Answer 1

Answer:

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:

• $x=-1,\:x=-9$

Step-by-step 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

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

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

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

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

solve

$x+5=\sqrt{16}$

$x+5=\sqrt{4^2}$

$x+5=4$

$x=-1$

also solving

$x+5=-\sqrt{16}$

$x+5=-4$

$x=-9$

Therefore, the solutions to the quadratic equation are:

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