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Sagot :
Given the Quadratic Equation:
[tex]x^2-14=11[/tex]You can solve it as follows:
1. Apply the Addition Property of Equality by adding 14 to both sides of the equation:
[tex]x^2-14+\((14)\)=11+(14)[/tex][tex]x^2=25[/tex]2. By definition, the square root undoes the effect of exponent 2 on the variable. Then, you have to take the square root of both sides of the equation:
[tex]\sqrt{x^2}=\pm\sqrt{25}[/tex][tex]x=\pm\sqrt{25}[/tex]3. Notice that you can split the equations into two equations:
[tex]x_1=\sqrt{25}[/tex][tex]x_2=-\sqrt{25}[/tex]4. Knowing that:
[tex]\sqrt{25}=5[/tex]You get:
[tex]x_1=\sqrt{25}=5[/tex][tex]x_2=-\sqrt{25}=-5[/tex]Hence, the answer is:
[tex]\begin{gathered} x_1=5 \\ x_2=-5 \end{gathered}[/tex]
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