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Simplifying 3x2 + -1024x + 12 = 0 Reorder the terms: 12 + -1024x + 3x2 = 0 Solving 12 + -1024x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -341.3333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -341.3333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -341.3333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -341.3333333x + x2 = 0 + -4 -341.3333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -341.3333333x + x2 = -4 The x term is -341.3333333x. Take half its coefficient (-170.6666667). Square it (29127.11112) and add it to both sides. Add '29127.11112' to each side of the equation. -341.3333333x + 29127.11112 + x2 = -4 + 29127.11112 Reorder the terms: 29127.11112 + -341.3333333x + x2 = -4 + 29127.11112 Combine like terms: -4 + 29127.11112 = 29123.11112 29127.11112 + -341.3333333x + x2 = 29123.11112 Factor a perfect square on the left side: (x + -170.6666667)(x + -170.6666667) = 29123.11112 Calculate the square root of the right side: 170.65494754 Break this problem into two subproblems by setting (x + -170.6666667) equal to 170.65494754 and -170.65494754.Subproblem 1
x + -170.6666667 = 170.65494754 Simplifying x + -170.6666667 = 170.65494754 Reorder the terms: -170.6666667 + x = 170.65494754 Solving -170.6666667 + x = 170.65494754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '170.6666667' to each side of the equation. -170.6666667 + 170.6666667 + x = 170.65494754 + 170.6666667 Combine like terms: -170.6666667 + 170.6666667 = 0.0000000 0.0000000 + x = 170.65494754 + 170.6666667 x = 170.65494754 + 170.6666667 Combine like terms: 170.65494754 + 170.6666667 = 341.32161424 x = 341.32161424 Simplifying x = 341.32161424Subproblem 2
x + -170.6666667 = -170.65494754 Simplifying x + -170.6666667 = -170.65494754 Reorder the terms: -170.6666667 + x = -170.65494754 Solving -170.6666667 + x = -170.65494754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '170.6666667' to each side of the equation. -170.6666667 + 170.6666667 + x = -170.65494754 + 170.6666667 Combine like terms: -170.6666667 + 170.6666667 = 0.0000000 0.0000000 + x = -170.65494754 + 170.6666667 x = -170.65494754 + 170.6666667 Combine like terms: -170.65494754 + 170.6666667 = 0.01171916 x = 0.01171916 Simplifying x = 0.01171916Solution
The solution to the problem is based on the solutions from the subproblems. x = {341.32161424, 0.01171916}
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