Find all values of x such that x^2-5x + 4=0. If you find more than one value, then list your solutions in increasing order, separated by commas.
(x-4)(x-1)=0
x=4, x=1 are solutions
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To find the values of x that satisfy the equation x^2 - 5x + 4 = 0, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this equation, the quadratic equation is written in the standard form ax^2 + bx + c = 0. In our case, a = 1, b = -5, and c = 4.
Substituting these values into the quadratic formula, we have:
x = (-(-5) ± sqrt((-5)^2 - 4*1*4)) / (2*1)
x = (5 ± sqrt(25 - 16)) / 2
x = (5 ± sqrt(9)) / 2
Taking the positive square root:
x = (5 + 3) / 2
x = 8 / 2
x = 4
Taking the negative square root:
x = (5 - 3) / 2
x = 2 / 2
x = 1
So, the values of x that satisfy the equation x^2 - 5x + 4 = 0 are x = 1 and x = 4. Therefore, the solutions in increasing order are:
x = 1, 4