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# complete the square

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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=???

Apr 27, 2020

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+21017
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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

Apr 27, 2020