Rewrite the equation by completing the square.
2 x^{2} -11 x +14 = 02x 2 −11x+14=02, x, squared, minus, 11, x, plus, 14, equals, 0 (x + {}(x+left parenthesis, x, plus )^2 = {}) 2 =right parenthesis, squared, equals
solve as in (x+???)^2=???
+23245 2x2 - 11x + 14 = 0
Move the constant term to the other side: 2x2 - 11x = -14
Divide all terms by the coefficient of the x2-term: x2 - (11/2)x = -7
Complete the square by
1) dividing the coefficient of the x-term by 2: (-11/2) / 2 = -11/4
2) squaring that number: (-11/4)2 = 121/16
3) adding this term to both sides of the equation: x2 - (11/2)x + 121/16 = -7 + 121/16
Factor and combine numbers: (x - 11/4)2 = 9/16
Find the square root of both sides: x - 11/4 = +/- 3/4
Finish: x - 11/4 = 3/4 x - 11/4 = -3/4
x = 14/4 x = 8/4
x = 7/2 x = 2
