(x^2+x-1/2)= x(x+1)-1/2 [x + (1 - square root of 3)/2][x + (1 + square root of 3)/2] = 0 Check it: x^2 + x/2 + (square root of 3)x)/2 + x/2 + 1/4 + (square root of 3)/4 - (square root of 3)x/2 - (square root of 3)/4 - 3/4 = 0 x^2 + x/2 + x/2 + [(square root of 3)x]/2 - [(square root of 3)x]/2 + (square root of 3)/4 - (square root of 3)/4 + 1/4 - 3/4 = 0 x^2 + x - 2/4 = 0 x^2 + x - 1/2 = 0 How to find this roots: Using the completing the square method: x^2 + x - 1/2 = 0 x^2 + x = 1/2 x^2 + x + 1/4 = 1/2 + 1/4 (x + 1/2)^2 = 3/4 x + 1/2 = (plus & minus)(square root of 3/4) x = -1/2 + (square root of 3)/2 x = - 1/2 - (square root of 3)/2
let f(x) = 3x^2 - 3x + 1. The roots of f is the same as asking for x where f(x) = 0. So we do it f(x) = 0, 3x^2 - 3x + 1 = 0. Using "complete the square" method 3(x^2 - x) + 1 = 0 3(x^2 + (2 . - 1/2 . x) + (-1/2)^2 -(-1/2)^2) + 1 = 0 3(x - 1/2)^2 -3/4 + 1 = 0 3(x - 1/2)^2 + 1/4 = 0 By the quadratic formula, the solution comes out to be x = [3+√(-3)]/6 and x = [3-√(-3)]/6 or x = (3+i√3)/6 and x = (3-i√3)/6 in other words, the solutions are complex numbers.
-1
2,430,090 = (2 x 106) + (4 x 105) + (3 x 104) + (0 x 103) + (0 x 102) + (9 x 101) + (0 x 100) or (2 x 1000000) + (4 x 100000) + (3 x 10000) + (0 x 1000) + (0 x 100) + (9 x 10) + (0 x 1)
-4
The answer to the math problem x 3-2x 2 plus x-4 0 is 0.
(x^2+x-1/2)= x(x+1)-1/2 [x + (1 - square root of 3)/2][x + (1 + square root of 3)/2] = 0 Check it: x^2 + x/2 + (square root of 3)x)/2 + x/2 + 1/4 + (square root of 3)/4 - (square root of 3)x/2 - (square root of 3)/4 - 3/4 = 0 x^2 + x/2 + x/2 + [(square root of 3)x]/2 - [(square root of 3)x]/2 + (square root of 3)/4 - (square root of 3)/4 + 1/4 - 3/4 = 0 x^2 + x - 2/4 = 0 x^2 + x - 1/2 = 0 How to find this roots: Using the completing the square method: x^2 + x - 1/2 = 0 x^2 + x = 1/2 x^2 + x + 1/4 = 1/2 + 1/4 (x + 1/2)^2 = 3/4 x + 1/2 = (plus & minus)(square root of 3/4) x = -1/2 + (square root of 3)/2 x = - 1/2 - (square root of 3)/2
x2 + x + 1 = 0 ∴ x2 + x + 1/4 = -3/4 ∴ (x + 1/2)2 = -3/4 ∴ x + 1/2 = ± √(-3/4) ∴ x = - 1/2 ± (i√3) / 2 ∴ x = (-1 ± i√3) / 2
-4
243,090 = (2 x 100000) + (4 x 10000) + (3 x 1000) + (0 x 100) + (9 x 10) + (0 x 1) OR (2 x 10^5) + (4 x 10^4) + (3 x 10^3) + (0 x 10^2) + (9 x 10^1) + (0 x 10^0)
(x^2+x-1/2)= x(x+1)-1/2 [x + (1 - square root of 3)/2][x + (1 + square root of 3)/2] = 0 Check it: x^2 + x/2 + (square root of 3)x)/2 + x/2 + 1/4 + (square root of 3)/4 - (square root of 3)x/2 - (square root of 3)/4 - 3/4 = 0 x^2 + x/2 + x/2 + [(square root of 3)x]/2 - [(square root of 3)x]/2 + (square root of 3)/4 - (square root of 3)/4 + 1/4 - 3/4 = 0 x^2 + x - 2/4 = 0 x^2 + x - 1/2 = 0 How to find this roots: Using the completing the square method: x^2 + x - 1/2 = 0 x^2 + x = 1/2 x^2 + x + 1/4 = 1/2 + 1/4 (x + 1/2)^2 = 3/4 x + 1/2 = (plus & minus)(square root of 3/4) x = -1/2 + (square root of 3)/2 x = - 1/2 - (square root of 3)/2
It is 0
x+x^2 = 12 x^2+x-12=0 (x+4)(x-3)=0 X = -4 or 3 Answer is 3. CHECK YOUR ANSWER: 3 + 3^2 = 3+9 = 12
2/3 +x= 4/6 4/6+x=4/6 x=0
2 x 2 + x - 1 = 0 4 + x - 1 = 0 4-1 + x = 0 3 + x = 0 3 + x - 3 = 0 - 3 x = -3 ---------- Another Solution Method (including text) for: 2 * 2 + x - 1 = 0 1. Do simple operations (*/+-) within from left to right: 2 * 2 + x - 1 = 0 4 + x - 1 = 0 3 + x = 0 2. Group like terms: - move numerical terms from the left side of the equal sign to the right side of the equal sign (remember to change the sign when moving from the left to the right of the equal sign): 3 + x = 0 x = 0 - 3 3. Do simple operations (^*/+-): x = 0 - 3 x = - 3
(3 x 103) + (0 x 102) + (2 x 101) + (4 x 100) OR (3 x 1000) + (0 x 100) + (2 x 10) + (4 x 1).
3x2 + 10x - 8 = 0 3x2 + 12x - 2x - 8 = 0 3x(x + 4) - 2(x + 4) = 0 (3x - 2)(x + 4) = 0 So 3x - 2 = 0 or x + 4 = 0 so x = 2/3 or x = -4