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Simplifying 12x2 + -1x + -45 = 0 Reorder the terms: -45 + -1x + 12x2 = 0 Solving -45 + -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'. -3.75 + -0.08333333333x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -0.08333333333x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -0.08333333333x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -0.08333333333x + x2 = 0 + 3.75 -0.08333333333x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -0.08333333333x + x2 = 3.75 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 = 3.75 + 0.001736111111 Reorder the terms: 0.001736111111 + -0.08333333333x + x2 = 3.75 + 0.001736111111 Combine like terms: 3.75 + 0.001736111111 = 3.751736111111 0.001736111111 + -0.08333333333x + x2 = 3.751736111111 Factor a perfect square on the left side: (x + -0.04166666667)(x + -0.04166666667) = 3.751736111111 Calculate the square root of the right side: 1.936939883 Break this problem into two subproblems by setting (x + -0.04166666667) equal to 1.936939883 and -1.936939883.Subproblem 1
x + -0.04166666667 = 1.936939883 Simplifying x + -0.04166666667 = 1.936939883 Reorder the terms: -0.04166666667 + x = 1.936939883 Solving -0.04166666667 + x = 1.936939883 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 = 1.936939883 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = 1.936939883 + 0.04166666667 x = 1.936939883 + 0.04166666667 Combine like terms: 1.936939883 + 0.04166666667 = 1.97860654967 x = 1.97860654967 Simplifying x = 1.97860654967Subproblem 2
x + -0.04166666667 = -1.936939883 Simplifying x + -0.04166666667 = -1.936939883 Reorder the terms: -0.04166666667 + x = -1.936939883 Solving -0.04166666667 + x = -1.936939883 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 = -1.936939883 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = -1.936939883 + 0.04166666667 x = -1.936939883 + 0.04166666667 Combine like terms: -1.936939883 + 0.04166666667 = -1.89527321633 x = -1.89527321633 Simplifying x = -1.89527321633Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.97860654967, -1.89527321633}
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