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Simplifying 24x2 + 8x + 2 = 5 + 6x Reorder the terms: 2 + 8x + 24x2 = 5 + 6x Solving 2 + 8x + 24x2 = 5 + 6x Solving for variable 'x'. Reorder the terms: 2 + -5 + 8x + -6x + 24x2 = 5 + 6x + -5 + -6x Combine like terms: 2 + -5 = -3 -3 + 8x + -6x + 24x2 = 5 + 6x + -5 + -6x Combine like terms: 8x + -6x = 2x -3 + 2x + 24x2 = 5 + 6x + -5 + -6x Reorder the terms: -3 + 2x + 24x2 = 5 + -5 + 6x + -6x Combine like terms: 5 + -5 = 0 -3 + 2x + 24x2 = 0 + 6x + -6x -3 + 2x + 24x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -3 + 2x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.125 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.08333333333x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.08333333333x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.08333333333x + x2 = 0 + 0.125 0.08333333333x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.08333333333x + x2 = 0.125 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 = 0.125 + 0.001736111111 Reorder the terms: 0.001736111111 + 0.08333333333x + x2 = 0.125 + 0.001736111111 Combine like terms: 0.125 + 0.001736111111 = 0.126736111111 0.001736111111 + 0.08333333333x + x2 = 0.126736111111 Factor a perfect square on the left side: (x + 0.04166666667)(x + 0.04166666667) = 0.126736111111 Calculate the square root of the right side: 0.356000156 Break this problem into two subproblems by setting (x + 0.04166666667) equal to 0.356000156 and -0.356000156.Subproblem 1
x + 0.04166666667 = 0.356000156 Simplifying x + 0.04166666667 = 0.356000156 Reorder the terms: 0.04166666667 + x = 0.356000156 Solving 0.04166666667 + x = 0.356000156 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 = 0.356000156 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = 0.356000156 + -0.04166666667 x = 0.356000156 + -0.04166666667 Combine like terms: 0.356000156 + -0.04166666667 = 0.31433348933 x = 0.31433348933 Simplifying x = 0.31433348933Subproblem 2
x + 0.04166666667 = -0.356000156 Simplifying x + 0.04166666667 = -0.356000156 Reorder the terms: 0.04166666667 + x = -0.356000156 Solving 0.04166666667 + x = -0.356000156 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 = -0.356000156 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = -0.356000156 + -0.04166666667 x = -0.356000156 + -0.04166666667 Combine like terms: -0.356000156 + -0.04166666667 = -0.39766682267 x = -0.39766682267 Simplifying x = -0.39766682267Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31433348933, -0.39766682267}
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