<PRE><B>Question 937693</B>
7x^2 - 21x - 3 = 0
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the above quadratic equation is in standard form, with a=7, b=-21 and c=-3
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
7 -21 -3
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the quadratic has two real roots at:
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x = 3.13663418
x = -0.1366342
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now solved by completing the square:
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7xx - 21x - 3 = 0
7xx - 21x = 3
(7xx - 21x = 3)/7
xx - 3x = 3/7
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complete the square:
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xx - 3x + (3/2)(3/2) = (3/7) + (3/2)(3/2)
(x - 3/2)^2 = (3/7) + (9/4)
(x - 3/2)^2 = (3*4/28) + (9*7/28)
(x - 3/2)^2 = (75/28)
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solve for x:
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sqrt( (x - 3/2)^2 ) = sqrt(75/28)
x - 3/2 = sqrt(75/28)
x = (+ or -) sqrt(75/28) + 3/2
x = +sqrt(75/28) + 3/2
x = -sqrt(75/28) + 3/2
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the quadratic has two real roots at:
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x = 3.13663418
x = -0.1366342
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