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1 = (1 + 4) ÷ (2 + 3) 2 = 4 - 3 + 2 - 1 3 = (4 + 3 - 1) ÷ 2 4 = (4 + 3 + 1) ÷ 2 5 = (4 x 2 - 3) x 1 6 = 4 + 3 - 2 + 1 7 = (4 + 3) x (2 - 1) 8 = 4 + 3 + 2 - 1 9 = 4 + 3 + 2 x 1 10 = 4 + 3 + 2 + 1 11 = 4 x 2 + 3 x 1 12 = 4 x 3 x (2 - 1) 13 = 3 x 4 + 2 - 1 14 = 3 x 4 + 2 x 1 15 = 3 x 4 + 2 + 1
2x2 = x+1 => 2x2-x-1= 0 Divide all terms by 2: x2-1/2x-1/2 = 0 Completing the square: (x-1/4)2-1/2 = 0 (x-1/4)2-1/2-1/16 = 0 (x-1/4)2-9/16 = 0 (x-1/4)2 = 9/16 Square root both sides: x-1/4 = -/+ 3/4 x = 1/4 -/+ 3/4 x = -1/2 and x = 1
x2-x-30 = (x-1/2)2 - 1/4 -30 as (a+b)2=a2+2ab+b2 with a=x then b=-1/2 = (x-1/2)2 - 121/4 = [(x-1/2)-sqrt(121/4)] [ [(x-1/2)+sqrt(121/4)] as a2-b2=(a-b)(a+b) then = (x-1/2-11/2)(x-1/2+11/2) = (x-6)(x+5)
5x2 + x - 4 = 0 a = 5, b = 1, c = -4 The equation of the axis of the symmetry of a parabola is x = - b/2a, which also is the x-coordinate of the vertex. x = - b/2a = - 1/2 Find the y-coordinate: f(x) = 5x2 + x - 4 f(-1/2) = 5(-1/2)2 + (-1/2) - 4 = 5(1/4) - 1/2 - 4 = 5/4 - 1/2 - 4 = 4/2 - 4 = 2 - 4 = -2 Thus, the vertex is (-1/2, -2).
X^2 + X = 0 halve the linear term (1) and square it then add to both sides X^2 + X + 1/4 = 1/4 factor left; gather terms right (X + 1/2)^2 = 1/4 (X + 1/2)^2 - 1/4 = 0 (-1/2,-1/4) vector and the number 1/4 was added to both sides completing the square