SOLUTION: Given the equation x^2 - 12x + -16y +84=0 , complete the square for both x and y. What is the result? How do I do this?

Question 932704: Given the equation x^2 - 12x + -16y +84=0 , complete the square for both x and y. What is the result? How do I do this?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x^2 - 12x - 16y + 84 = 0
16y = x^2 - 12x + 84
y = (1/16)x^2 - (12/16)x + (84/16)
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(1/16)x^2 - (12/16)x + (84/16) = 0
x^2 - 12x + 84 = 0
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the above quadratic equation is in standard form, with a=1, b=-12 and c=84
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -12 84
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two complex roots at:
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answer by matrix method:
x = 6 + (6.92820323)i
x = 6 - (6.92820323)i
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now solved by completing the square:
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x^2 - 12x + 84 = 0
x^2 - 12x = -84
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complete the square by adding Z to both sides:
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x^2 - 12x + Z = -84 + Z
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what is Z? ... Z is the square of 1/2 the coefficient of the x term:
Z = ( (1/2)(-12) )^2 = (-6)^2 = 36
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x^2 - 12x + 36 = -84 + 36
(x - 6)(x - 6) = -48
(x - 6)^2 = -48
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solve for x:
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recall that if u^2=v then u=+sqrt(v) or u=-sqrt(v)
recall that sqrt(-1) = i
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(x - 6)^2 = -48
sqrt( (x - 6)^2 ) = sqrt( -48 )
x - 6 = +- sqrt( -48 )
x - 6 = +- sqrt( -4*4*3 )
x - 6 = +- 4 * sqrt( -3 )
x - 6 = +- 4 * sqrt( 3 )i
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x = 6 +- 4 * sqrt( 3 )i
x = 6 +- (6.92820323)i
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answer by completing the square:
x = 6 + (6.92820323)i
x = 6 - (6.92820323)i
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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