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Simplifying 24x2 + 47x + 2 = 0 Reorder the terms: 2 + 47x + 24x2 = 0 Solving 2 + 47x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.08333333333 + 1.958333333x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + 1.958333333x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + 1.958333333x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + 1.958333333x + x2 = 0 + -0.08333333333 1.958333333x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 1.958333333x + x2 = -0.08333333333 The x term is 1.958333333x. Take half its coefficient (0.9791666665). Square it (0.9587673608) and add it to both sides. Add '0.9587673608' to each side of the equation. 1.958333333x + 0.9587673608 + x2 = -0.08333333333 + 0.9587673608 Reorder the terms: 0.9587673608 + 1.958333333x + x2 = -0.08333333333 + 0.9587673608 Combine like terms: -0.08333333333 + 0.9587673608 = 0.87543402747 0.9587673608 + 1.958333333x + x2 = 0.87543402747 Factor a perfect square on the left side: (x + 0.9791666665)(x + 0.9791666665) = 0.87543402747 Calculate the square root of the right side: 0.935646315 Break this problem into two subproblems by setting (x + 0.9791666665) equal to 0.935646315 and -0.935646315.Subproblem 1
x + 0.9791666665 = 0.935646315 Simplifying x + 0.9791666665 = 0.935646315 Reorder the terms: 0.9791666665 + x = 0.935646315 Solving 0.9791666665 + x = 0.935646315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9791666665' to each side of the equation. 0.9791666665 + -0.9791666665 + x = 0.935646315 + -0.9791666665 Combine like terms: 0.9791666665 + -0.9791666665 = 0.0000000000 0.0000000000 + x = 0.935646315 + -0.9791666665 x = 0.935646315 + -0.9791666665 Combine like terms: 0.935646315 + -0.9791666665 = -0.0435203515 x = -0.0435203515 Simplifying x = -0.0435203515Subproblem 2
x + 0.9791666665 = -0.935646315 Simplifying x + 0.9791666665 = -0.935646315 Reorder the terms: 0.9791666665 + x = -0.935646315 Solving 0.9791666665 + x = -0.935646315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9791666665' to each side of the equation. 0.9791666665 + -0.9791666665 + x = -0.935646315 + -0.9791666665 Combine like terms: 0.9791666665 + -0.9791666665 = 0.0000000000 0.0000000000 + x = -0.935646315 + -0.9791666665 x = -0.935646315 + -0.9791666665 Combine like terms: -0.935646315 + -0.9791666665 = -1.9148129815 x = -1.9148129815 Simplifying x = -1.9148129815Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0435203515, -1.9148129815}
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