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Khan Academy please show work​

Khan Academy please show work​-example-1

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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

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

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