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Simplifying 6x2 + -0.5x + -210 = 0 Reorder the terms: -210 + -0.5x + 6x2 = 0 Solving -210 + -0.5x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -35 + -0.08333333333x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -0.08333333333x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -0.08333333333x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -0.08333333333x + x2 = 0 + 35 -0.08333333333x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -0.08333333333x + x2 = 35 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 = 35 + 0.001736111111 Reorder the terms: 0.001736111111 + -0.08333333333x + x2 = 35 + 0.001736111111 Combine like terms: 35 + 0.001736111111 = 35.001736111111 0.001736111111 + -0.08333333333x + x2 = 35.001736111111 Factor a perfect square on the left side: (x + -0.04166666667)(x + -0.04166666667) = 35.001736111111 Calculate the square root of the right side: 5.916226509 Break this problem into two subproblems by setting (x + -0.04166666667) equal to 5.916226509 and -5.916226509.Subproblem 1
x + -0.04166666667 = 5.916226509 Simplifying x + -0.04166666667 = 5.916226509 Reorder the terms: -0.04166666667 + x = 5.916226509 Solving -0.04166666667 + x = 5.916226509 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 = 5.916226509 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = 5.916226509 + 0.04166666667 x = 5.916226509 + 0.04166666667 Combine like terms: 5.916226509 + 0.04166666667 = 5.95789317567 x = 5.95789317567 Simplifying x = 5.95789317567Subproblem 2
x + -0.04166666667 = -5.916226509 Simplifying x + -0.04166666667 = -5.916226509 Reorder the terms: -0.04166666667 + x = -5.916226509 Solving -0.04166666667 + x = -5.916226509 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 = -5.916226509 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = -5.916226509 + 0.04166666667 x = -5.916226509 + 0.04166666667 Combine like terms: -5.916226509 + 0.04166666667 = -5.87455984233 x = -5.87455984233 Simplifying x = -5.87455984233Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.95789317567, -5.87455984233}
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