Question 331423
2x^2-3x=5 completing the square
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We need the coefficient of x^2, to be 1, divide each term by 2, and you have
x^2 - {{{3/2}}}x = {{{5/2}}}
:
x^2 - {{{3/2}}}x + ____ = {{{5/2}}}
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{{{(3/4)^2}}} will complete the square. add to both sides
x^2 - {{{3/2}}}x + {{{9/16}}} = {{{5/2}}} + {{{9/16}}}
:
x^2 - {{{3/2}}}x + {{{9/16}}} = {{{40/16}}} + {{{9/16}}}
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x^2 - {{{3/2}}}x + {{{9/16}}} = {{{49/16}}}
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(x - {{{3/4}}})^2 = {{{49/16}}}
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Find the square root of both sides
x - {{{3/4}}} = +/-{{{sqrt(49/16)}}}
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x = {{{3/4}}} +/-{{{sqrt(49/16)}}}
a perfect square
x = {{{3/4}}} +/-{{{7/4}}}
Two solutions
x = {{{3/4}}} + {{{7/4}}}
x = {{{10/4}}}
x = 2{{{1/2}}}
and
x = {{{3/4}}} - {{{7/4}}}
x = {{{-4/4}}}
x = -1
:
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Check solution in original equation using x=2.5
2(2.5^2) -3(2.5) = 5 
2(6.25) - 7.5 = 5
12.5 - 7.5 = 5; confirms our solution,
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You can check solution for x=-1