solve $x^{2}=12x - 15$ by completing the square. which is the solution set of the equation?\n{-6…

solve $x^{2}=12x - 15$ by completing the square. which is the solution set of the equation?\n{-6 - $sqrt{51}$, -6 + $sqrt{51}$}\n{-6 - $sqrt{21}$, -6 + $sqrt{21}$}\n{6 - $sqrt{51}$, 6 + $sqrt{51}$}\n{6 - $sqrt{21}$, 6 + $sqrt{21}$}

solve $x^{2}=12x - 15$ by completing the square. which is the solution set of the equation?\n{-6 - $sqrt{51}$, -6 + $sqrt{51}$}\n{-6 - $sqrt{21}$, -6 + $sqrt{21}$}\n{6 - $sqrt{51}$, 6 + $sqrt{51}$}\n{6 - $sqrt{21}$, 6 + $sqrt{21}$}

Answer

Explanation:

Step1: Rearrange the equation

$x^{2}-12x=- 15$

Step2: Complete the square on the left - hand side

The coefficient of $x$ is $-12$. Half of it is $\frac{-12}{2}=-6$, and its square is $(-6)^{2} = 36$. Add 36 to both sides of the equation: $x^{2}-12x + 36=-15 + 36$ $(x - 6)^{2}=21$

Step3: Solve for $x$

Take the square root of both sides: $x-6=\pm\sqrt{21}$ $x = 6\pm\sqrt{21}$

Answer:

{6 - $\sqrt{21}$, 6 + $\sqrt{21}$}