Answer:
The solution set of the equation are (2,0) and (-12,0)
Step-by-step explanation:
Given : Equation [tex]x^2+10x=24[/tex]
To find : Solve equation by completing the square ?
Solution :
The general form of quadratic equation is [tex]ax^2+bx+c=0[/tex]
So, [tex]x^2+10x-24=0[/tex]
To complete the square we add and subtract [tex](\frac{b}{2})^2[/tex]
i.e. [tex](\frac{b}{2})^2=(\frac{10}{2})^2=5^2[/tex]
Applying in equation,
[tex]x^2+10x-24+5^2-5^2=0[/tex]
Re-writ equation as,
[tex]x^2+2\times 5\times x+5^2-24-25=0[/tex]
Apply [tex]a^2+2ab+b^2=(a+b)^2[/tex]
[tex](x+5)^2-49=0[/tex]
[tex](x+5)^2=49[/tex]
Taking root both side,
[tex]x+5=\pm \sqrt{49}[/tex]
[tex]x+5=\pm 7[/tex]
[tex]x+5=7[/tex] or [tex]x+5=-7[/tex]
[tex]x=2[/tex] or [tex]x=-12[/tex]
Therefore, the solution set of the equation are (2,0) and (-12,0)
Answer:
The correct answer is C!!!
I hope this helps you out, have an amazing day
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