x + 77 = 3(x - 6)
x + 77 = 3x - 18
x + 77 + 18 = 3x - 18 + 18
x + 95 = 3x
x + 95 - x = 3x - x
95 = 2x
x = 95/2
x = 47.5
Identity property of zero states that the sum of 0 and any number is that number.
We can solve this by using the formula:
(x, y) (x + a, y + b) = (5,-4) (-2,1)
So, plugging in the values and solving for a and b,
5 + a = -2
a = -8
-4 + b = 1
b = 5
Therefore, the translation is
(x,y) (x - 8, y +5)
<span>divide both sides of the equation by 2 to get:
(x + 1/4)^2 = -7/16 ***** this is your solution.
continue further to solve for x if you care to, but the problem did not require you to do this.
take the square root of both sides of the equation to get:
x + 1/4 = plus or minus sqrt(-7/16)
subtract 1/4 from both sides of the equation to get x = -1/4 plus or minus sqrt(-7/16).
since sqrt(-7/16) is the same as sqrt(7/16) * i, your solution becomes:
x = -1/4 plus or minus sqrt(7/16) * i.
your problem was to convert it to the form of (x + p)2 = q.
the solution to that is:
</span><span>(x + 1/4)^2 = -7/16 </span><span>subtract 1 from both sides of the equation to get:
2x^2 + x = -1
factor out a 2 on the left side of the equation to get:
2 * (x^2 + x/2) = -1
complete the squares on x^2 + x/2 to get:
2 * ((x+1/4)^2 - (1/16)) = -1
simplify by distibuting the multiplication to get:
2 * (x+1/4)^2 - 2*(1/16) = -1
simplify further to get:
2 * (x+1/4)^2 - 1/8 = -1
add 1/8 to both sides of the equation to get:
2 * (x + 1/4)^2 = -7/8 .
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