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Simplifying 3x + -4x + -3 = 12x2 + -6 Reorder the terms: -3 + 3x + -4x = 12x2 + -6 Combine like terms: 3x + -4x = -1x -3 + -1x = 12x2 + -6 Reorder the terms: -3 + -1x = -6 + 12x2 Solving -3 + -1x = -6 + 12x2 Solving for variable 'x'. Reorder the terms: -3 + 6 + -1x + -12x2 = -6 + 12x2 + 6 + -12x2 Combine like terms: -3 + 6 = 3 3 + -1x + -12x2 = -6 + 12x2 + 6 + -12x2 Reorder the terms: 3 + -1x + -12x2 = -6 + 6 + 12x2 + -12x2 Combine like terms: -6 + 6 = 0 3 + -1x + -12x2 = 0 + 12x2 + -12x2 3 + -1x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 3 + -1x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.25 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.08333333333x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.08333333333x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.08333333333x + x2 = 0 + 0.25 0.08333333333x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.08333333333x + x2 = 0.25 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 = 0.25 + 0.001736111111 Reorder the terms: 0.001736111111 + 0.08333333333x + x2 = 0.25 + 0.001736111111 Combine like terms: 0.25 + 0.001736111111 = 0.251736111111 0.001736111111 + 0.08333333333x + x2 = 0.251736111111 Factor a perfect square on the left side: (x + 0.04166666667)(x + 0.04166666667) = 0.251736111111 Calculate the square root of the right side: 0.501733107 Break this problem into two subproblems by setting (x + 0.04166666667) equal to 0.501733107 and -0.501733107.Subproblem 1
x + 0.04166666667 = 0.501733107 Simplifying x + 0.04166666667 = 0.501733107 Reorder the terms: 0.04166666667 + x = 0.501733107 Solving 0.04166666667 + x = 0.501733107 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 = 0.501733107 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = 0.501733107 + -0.04166666667 x = 0.501733107 + -0.04166666667 Combine like terms: 0.501733107 + -0.04166666667 = 0.46006644033 x = 0.46006644033 Simplifying x = 0.46006644033Subproblem 2
x + 0.04166666667 = -0.501733107 Simplifying x + 0.04166666667 = -0.501733107 Reorder the terms: 0.04166666667 + x = -0.501733107 Solving 0.04166666667 + x = -0.501733107 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 = -0.501733107 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = -0.501733107 + -0.04166666667 x = -0.501733107 + -0.04166666667 Combine like terms: -0.501733107 + -0.04166666667 = -0.54339977367 x = -0.54339977367 Simplifying x = -0.54339977367Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.46006644033, -0.54339977367}
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