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
14
The equation is equivalent to: -3x2 - 12x - 1 = 0 [you could change signs to get 3x2 + 12x + 1 = 0 but that is not required] The discriminant is (-12)2 - 4*(-3)(-1) = 144 - 12 = 132
2*2 - 12x +16 =0 4 - 12x +16 =0 -12x + 16 +4 =0 -12x + 20 =0 -12x = -20 x = 1.666666667
12x-4y+9z+2y =12x-2y+9z
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.
I assume you mean,X2 + 12X - 5 = 0X2 + 12X = 5Now, halve the linear term (12), square it and add it to both sidesX2 + 12X + 36 = 5 + 36factor on the left, gather terms on the right(X + 6)2 = 41(X + 6)2 - 41 = 0==============vertex form.... (- 6, - 41)========================--------------vertexAnd that number added is 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).