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Simplifying 12 + -1x + -12(x * x) = 0 Multiply x * x 12 + -1x + -12(x2) = 0 Solving 12 + -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'. -1 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.08333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.08333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.08333333333x + x2 = 0 + 1 0.08333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.08333333333x + x2 = 1 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 = 1 + 0.001736111111 Reorder the terms: 0.001736111111 + 0.08333333333x + x2 = 1 + 0.001736111111 Combine like terms: 1 + 0.001736111111 = 1.001736111111 0.001736111111 + 0.08333333333x + x2 = 1.001736111111 Factor a perfect square on the left side: (x + 0.04166666667)(x + 0.04166666667) = 1.001736111111 Calculate the square root of the right side: 1.000867679 Break this problem into two subproblems by setting (x + 0.04166666667) equal to 1.000867679 and -1.000867679.Subproblem 1
x + 0.04166666667 = 1.000867679 Simplifying x + 0.04166666667 = 1.000867679 Reorder the terms: 0.04166666667 + x = 1.000867679 Solving 0.04166666667 + x = 1.000867679 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 = 1.000867679 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = 1.000867679 + -0.04166666667 x = 1.000867679 + -0.04166666667 Combine like terms: 1.000867679 + -0.04166666667 = 0.95920101233 x = 0.95920101233 Simplifying x = 0.95920101233Subproblem 2
x + 0.04166666667 = -1.000867679 Simplifying x + 0.04166666667 = -1.000867679 Reorder the terms: 0.04166666667 + x = -1.000867679 Solving 0.04166666667 + x = -1.000867679 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 = -1.000867679 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = -1.000867679 + -0.04166666667 x = -1.000867679 + -0.04166666667 Combine like terms: -1.000867679 + -0.04166666667 = -1.04253434567 x = -1.04253434567 Simplifying x = -1.04253434567Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.95920101233, -1.04253434567}
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