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Simplifying 12x2 + -1x + -48 = 0 Reorder the terms: -48 + -1x + 12x2 = 0 Solving -48 + -1x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4 + -0.08333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.08333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.08333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.08333333333x + x2 = 0 + 4 -0.08333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.08333333333x + x2 = 4 The x term is -0.08333333333x. Take half its coefficient (-0.04166666667). Square it (0.001736111111) and add it to both sides. Add '0.001736111111' to each side of the equation. -0.08333333333x + 0.001736111111 + x2 = 4 + 0.001736111111 Reorder the terms: 0.001736111111 + -0.08333333333x + x2 = 4 + 0.001736111111 Combine like terms: 4 + 0.001736111111 = 4.001736111111 0.001736111111 + -0.08333333333x + x2 = 4.001736111111 Factor a perfect square on the left side: (x + -0.04166666667)(x + -0.04166666667) = 4.001736111111 Calculate the square root of the right side: 2.000433981 Break this problem into two subproblems by setting (x + -0.04166666667) equal to 2.000433981 and -2.000433981.Subproblem 1
x + -0.04166666667 = 2.000433981 Simplifying x + -0.04166666667 = 2.000433981 Reorder the terms: -0.04166666667 + x = 2.000433981 Solving -0.04166666667 + x = 2.000433981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = 2.000433981 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = 2.000433981 + 0.04166666667 x = 2.000433981 + 0.04166666667 Combine like terms: 2.000433981 + 0.04166666667 = 2.04210064767 x = 2.04210064767 Simplifying x = 2.04210064767Subproblem 2
x + -0.04166666667 = -2.000433981 Simplifying x + -0.04166666667 = -2.000433981 Reorder the terms: -0.04166666667 + x = -2.000433981 Solving -0.04166666667 + x = -2.000433981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = -2.000433981 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = -2.000433981 + 0.04166666667 x = -2.000433981 + 0.04166666667 Combine like terms: -2.000433981 + 0.04166666667 = -1.95876731433 x = -1.95876731433 Simplifying x = -1.95876731433Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.04210064767, -1.95876731433}
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