1. First, ensure the coefficient of the x* term is 1. In this case, the coefficient is already 1.
2. Rewrite the equation in the form:
x* + 6x = 59.
3. To complete the square, take half of the coefficient of x (which is 3 in this case), square it (which gives 9), and add and subtract this value inside the parentheses: x + 6x+9-
9 = 59.
4. Rearrange the equation: (x + 3)2=
68.
5. Take the square root of both sides: x+ 3=+v68.
6. Simplify the square root of 68 to
2V17: x + 3 = +2 V17.
7. Solve for x: x = -3 ÷ 2v17.
Therefore, the solutions to the
quadratic equation x + 6x - 59 = 0
by completing the square are x= -3 +
2V17 and x = -3 - 2V17.
