Choose and apply the best method to solve the given quadratic equation.
$x^2-6x=5$

• A. $x=6+\sqrt{14},x=6-\sqrt{14}$
• B. $x=10,x=-4$
• C. $x=3+\sqrt{14},x=3-\sqrt{14}$
• D. $x=6,x=0$

Answer: (C)

Verified step by step guidance

1. Start by rewriting the given quadratic equation in standard form, which is ax^2 + bx + c = 0. The given equation is x^2 - 6x = 5. Subtract 5 from both sides to get x^2 - 6x - 5 = 0.
2. Identify the coefficients a, b, and c from the standard form equation x^2 - 6x - 5 = 0. Here, a = 1, b = -6, and c = -5.
3. Use the quadratic formula to find the solutions for x. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).
4. Substitute the values of a, b, and c into the quadratic formula: x = (6 ± √((-6)^2 - 4 * 1 * (-5))) / (2 * 1).
5. Simplify the expression under the square root and then solve for x using the plus and minus signs to find the two possible solutions.