Solve the following quadratic equation by completing the square. x 2 −8x+5=0

Step 1: Write down the given equation: x^2 - 8x + 5 = 0

Step 2: Rearrange the equation so that the x^2 and x terms are on one side and the constant is on the other side: x^2 - 8x = -5

Step 3: To complete the square, we need to add the square of half the coefficient of x to both sides of the equation. Half of -8 is -4, and (-4)^2 = 16. So, we add 16 to both sides: x^2 - 8x + 16 = -5 + 16

Step 4: Simplify both sides of the equation: (x - 4)^2 = 11

Step 5: Take the square root of both sides. Remember to consider both the positive and negative roots: x - 4 = ± √11

Step 6: Solve for x by adding 4 to both sides: x = 4 ± √11

So, the solutions to the equation x^2 - 8x + 5 = 0 are x = 4 + √11 and x = 4 - √11.