I assume you mean,
X2 + 12X - 5 = 0
X2 + 12X = 5
Now, halve the linear term (12), square it and add it to both sides
X2 + 12X + 36 = 5 + 36
factor on the left, gather terms on the right
(X + 6)2 = 41
(X + 6)2 - 41 = 0
==============vertex form.... (- 6, - 41)
========================--------------vertex
And that number added is 36
You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.
The constant term - the part without a variable - must be equal to the square of one half the linear term - the number in front of the "x". That is, it must be (12/2)2 = 36.
36.1. You take the coefficient of x : = 122. Halve it : = 63. Then square it : = 364. Add it.This gives x2 + 12x + 36 = (x + 6)2The above method only works if the coefficient of x2 is 1. If it is not then the processs is slightly more complicated.
x2 + 12x - 11 = x2 + 12x + (12/2)2 - (12/2)2 - 11 = (x + 6)2 - 47
There is no answer to this problem unless x is 0. For the suare root of 98x to be a real number, x has to be positive or zero. For the square root of -147x to be a real number, x has to be negative or zero. Seeing has x has to fit both requirements, the problem has an answer only if x is zero.
The idea is to take half the linear part (12, in this case), then square it. The constant part must be equal to this result.
You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.
9
The constant term - the part without a variable - must be equal to the square of one half the linear term - the number in front of the "x". That is, it must be (12/2)2 = 36.
x^2 + 12x = 5 x^2 + 12x + __ = 5 + __ x^2 + 12x + 36 = 5 + 36 (The 36 I got from taking half of 12 and then squaring that number (which is 6).) (x + 6)^2 = 41 x + 6 = (the square root of 41) x = (the square root of 41) - 6. Hope that helped :)
x2 - 12x + 36 = (x - 6)2
Add? I will show you the process. X^2 + 12X = 16 halve the linear term (12), square it and ADD it to both sides X^2 + 12X + 36 = 16 + 36 factor the right side; gather terms right (X + 6)^2 = 52 (X + 6)^2 - 52 = 0 (-6,-52) vertex of function As you see 36 was added to both sides
168 square feet
x2 + 12x - 5 = 0x2 + 12x - 5 + 5 = 0 + 5x2 + 12x = 5x2 + 12x + (12/2)2 = 5 + (12/2)2x2 + 12x + (6)2 = 5 + 36(x + 6)2 = 41 (square root of both sides)x + 6 = ± √41x + 6 - 6 = -6 ± √41x = -6 ± √41x ≈ -6 + 6.4 = -0.4x ≈ -6 - 6.4 = -12.4
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2 root 3x
Yes, it is the square of (3x + 2). 3x is the square root of 9x2; 4 is the square of 2; to check whether it is a perfect square, the center term must be twice (3x times 2).