Checking Quadratic Equation? x²+10x=-8 My solution is ±√(17) -5

[Ebba Sen Pai]

Checking Quadratic Equation? x²+10x=-8 My solution is ±√(17) -5

I do not understand how to check quadratic equations when "plugging in" the solution(s) I have. My problem is that when I plug in a solution I have ahieved which I know to be correct, Symbolab tells me the equation I have provided is not true. For instance

x²+10x=-8
My solution is ±√(17) -5

If however I try to "plug in" my solution into the original equation, I am told that it is not a true statement.

[±√(17) -5]²+10[±√(17) -5]=-8

My humblest gratitude for any assistance. Everything else about quadratics has made sense to me. This is the first time that the "checking" phase is what is stumping me :-?
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[Dr.Peterson]

I do not understand how to check quadratic equations when "plugging in" the solution(s) I have. My problem is that when I plug in a solution I have ahieved which I know to be correct, Symbolab tells me the equation I have provided is not true. For instance

x²+10x=-8
My solution is ±√(17) -5

If however I try to "plug in" my solution into the original equation, I am told that it is not a true statement.

[±√(17) -5]²+10[±√(17) -5]=-8

My humblest gratitude for any assistance. Everything else about quadratics has made sense to me. This is the first time that the "checking" phase is what is stumping me :-?

Plug in only one solution at a time! It is probably getting confused:

[√(17) -5]²+10[√(17) -5]=-8
[-√(17) -5]²+10[-√(17) -5]=-8

 

[Ebba Sen Pai]

Plug in only one solution at a time! It is probably getting confused:

[√(17) -5]²+10[√(17) -5]=-8
[-√(17) -5]²+10[-√(17) -5]=-8

Thank you Dr Peterson! My sincerest gratitude! I really apreicate it! I feel so silly that I didn't recognize this.

 

[JeffM]

I do not understand how to check quadratic equations when "plugging in" the solution(s) I have. My problem is that when I plug in a solution I have ahieved which I know to be correct, Symbolab tells me the equation I have provided is not true. For instance

x²+10x=-8
My solution is ±√(17) -5

If however I try to "plug in" my solution into the original equation, I am told that it is not a true statement.

[±√(17) -5]²+10[±√(17) -5]=-8

My humblest gratitude for any assistance. Everything else about quadratics has made sense to me. This is the first time that the "checking" phase is what is stumping me :-?

Doing arithmetic involving the \(\displaystyle \pm\) sign is highly prone to sign errors.

\(\displaystyle (\pm \sqrt{17} - 5)^2 + 10(\pm \sqrt{17} - 5) =\)

\(\displaystyle \{ (\pm \sqrt{17})^2 + 2( \pm \sqrt{17})(-\ 5) + (-\ 5)^2\} \pm 10\sqrt{17} - 50 =\)

\(\displaystyle 17 + \mp 10\sqrt{17} + 25 \pm 10\sqrt{17} - 50 = 42 - 50 = -\ 8.\)

But it is very easy to make a mistake and go

\(\displaystyle 2( \pm \sqrt{17})(-\ 5) = 10\ \pm \sqrt{17}.\)

As Dr. P says, check one of the solutions by itself.

\(\displaystyle (\sqrt{17} - 5)^2 + 10(\sqrt{17} - 5) = 17 + 2(\sqrt{17})(-\ 5) + 25 + 10\sqrt{17} - 50 =\)

\(\displaystyle 42 - 50 - 10\sqrt{17} + 10\sqrt{17} = - \ 8.\)

Then check the other solution.

 

[Steven G]

If however I try to "plug in" my solution into the original equation, I am told that it is not a true statement.

Not solutions, but solutions. As pointed out, check one at a time or be very careful