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.
