Question

solve $x^2 - 8x = 3$ by completing the square. which is the solution set of the equation? \\{4 - \sqrt{19}, 4 + \sqrt{19}\\} \\{4 - \sqrt{3}, 4 + \sqrt{3}\\} \\{4 - \sqrt{11}, 4 + \sqrt{11}\\}

Explanation:

Step1: Rearrange equation to standard form

$x^2 - 8x - 3 = 0$

Step2: Complete the square for $x$ terms

$x^2 - 8x + 16 = 3 + 16$

Step3: Rewrite as perfect square

$(x - 4)^2 = 19$

Step4: Take square root of both sides

$x - 4 = \pm\sqrt{19}$

Step5: Solve for $x$

$x = 4 \pm\sqrt{19}$

Answer:

$\{4 - \sqrt{19}, 4 + \sqrt{19}\}$