Solve the equation. (Enter solutions from smallest to largest. If there is no solution, enter NONE in the answer boxes.)
x2 - 5x + 5 = 0
x =
x =
To solve the equation x^2 - 5x + 5 = 0, we can use the quadratic formula. The quadratic formula states that for any equation in the form ax^2 + bx + c = 0, the solutions (or roots) can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -5, and c = 5. Plugging these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4(1)(5))) / (2(1))
x = (5 ± √(25 - 20)) / 2
x = (5 ± √5) / 2
Therefore, the solutions to the equation x^2 - 5x + 5 = 0 are x = (5 + √5) / 2 and x = (5 - √5) / 2.
Writing them in order from smallest to largest, the solutions are:
x = (5 - √5) / 2
x = (5 + √5) / 2