Final answer:
To solve the equation x²-10x+25=3, we can use factoring or the quadratic formula. Factoring is not possible in this case, so we will use the quadratic formula to find the solutions. The solutions are x = 5 + √3 and x = 5 - √3.
Step-by-step explanation:
To solve the equation x²-10x+25=3 by factoring, we need to bring all the terms to one side of the equation to create a quadratic expression equal to zero.
x² - 10x + 25 - 3 = 0
Combining like terms, we simplify the equation to:
x² - 10x + 22 = 0
Now, we need to factor the quadratic expression. However, this quadratic equation cannot be easily factored, so we need to use the quadratic formula. The quadratic formula is: x = (-b ± √(b² - 4ac)) / 2a.
Plugging in the values from the equation, we get:
x = (-(-10) ± √((-10)² - 4(1)(22))) / (2(1))
Simplifying further:
x = (10 ± √(100 - 88)) / 2
x = (10 ± √12) / 2
x = (10 ± 2√3) / 2
x = 5 ± √3
Therefore, the solutions to the equation are x = 5 + √3 and x = 5 - √3.