Solve the equation. (Enter solutions from smallest to largest. If there is no solution, enter NONE in the answer boxes.)
x2 - 5x + 5 = 0
Hint: use the quadratic formula.
x = [-b +- sqrt(b^2 - 4ac)]/(2a)
In your case,
a = 1, b = -5, and c = 5.
To solve the quadratic equation x^2 - 5x + 5 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions (or roots) are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation x^2 - 5x + 5 = 0, we can identify that 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)
= (5 ± √(25 - 20)) / 2
= (5 ± √5) / 2
Therefore, the solutions to the equation x^2 - 5x + 5 = 0 are:
x = (5 + √5) / 2
x = (5 - √5) / 2
Remember to enter the solutions from smallest to largest, so the final answer would be:
x = (5 - √5) / 2, (5 + √5) / 2