Question

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

Explanation:

Step1: Rearrange to standard form

$x^2 - 12x + 15 = 0$

Step2: Isolate variable terms

$x^2 - 12x = -15$

Step3: Complete the square

$x^2 -12x + 36 = -15 + 36$
$(x-6)^2 = 21$

Step4: Solve for x

$x - 6 = \pm\sqrt{21}$
$x = 6 \pm\sqrt{21}$

Answer:

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