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Sagot :
Answer:
(x-2)^2=25
Explanation:
Given the below quadratic equation;
[tex]x^2-4x+3=24[/tex]To rewrite by completing the square, the 1st step is to subtract 3 from both sides of the equation;
[tex]\begin{gathered} x^2-4x+3-3=24-3 \\ x^2-4x=21 \end{gathered}[/tex]The 2nd step is to add half of the coefficient of x squared to both sides of the equation;
[tex]\begin{gathered} x^2-4x+(-_{}\frac{1}{2}\ast4)^2=21+(-\frac{1}{2}\ast4)^2 \\ x^2-4x+(-2)^2=21+(-2)^2 \\ x^2-4x+4=21+4 \\ x^2-4x+4=25 \end{gathered}[/tex]We can then factor the perfect square as;
[tex](x-2)^2=25_{}[/tex]To find the solutions of the equation, we have to take the square root of both sides of the equation;
[tex]\begin{gathered} \sqrt[]{(x-2)^2}=\sqrt[]{25} \\ x-2=\frac{+}{-}5 \end{gathered}[/tex]For x 1;
[tex]x_1=+5+2=7[/tex]For x2;
[tex]x_2=-5+2=-3_{}[/tex]So x1 = 7 and x2 = -3.
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