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Simplifying 0.5x + 2 = 12x(3x) Reorder the terms: 2 + 0.5x = 12x(3x) Remove parenthesis around (3x) 2 + 0.5x = 12x * 3x Reorder the terms for easier multiplication: 2 + 0.5x = 12 * 3x * x Multiply 12 * 3 2 + 0.5x = 36x * x Multiply x * x 2 + 0.5x = 36x2 Solving 2 + 0.5x = 36x2 Solving for variable 'x'. Combine like terms: 36x2 + -36x2 = 0 2 + 0.5x + -36x2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -0.05555555556 + -0.01388888889x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + -0.01388888889x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + -0.01388888889x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + -0.01388888889x + x2 = 0 + 0.05555555556 -0.01388888889x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 -0.01388888889x + x2 = 0.05555555556 The x term is -0.01388888889x. Take half its coefficient (-0.006944444445). Square it (0.00004822530865) and add it to both sides. Add '0.00004822530865' to each side of the equation. -0.01388888889x + 0.00004822530865 + x2 = 0.05555555556 + 0.00004822530865 Reorder the terms: 0.00004822530865 + -0.01388888889x + x2 = 0.05555555556 + 0.00004822530865 Combine like terms: 0.05555555556 + 0.00004822530865 = 0.05560378086865 0.00004822530865 + -0.01388888889x + x2 = 0.05560378086865 Factor a perfect square on the left side: (x + -0.006944444445)(x + -0.006944444445) = 0.05560378086865 Calculate the square root of the right side: 0.23580454 Break this problem into two subproblems by setting (x + -0.006944444445) equal to 0.23580454 and -0.23580454.Subproblem 1
x + -0.006944444445 = 0.23580454 Simplifying x + -0.006944444445 = 0.23580454 Reorder the terms: -0.006944444445 + x = 0.23580454 Solving -0.006944444445 + x = 0.23580454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006944444445' to each side of the equation. -0.006944444445 + 0.006944444445 + x = 0.23580454 + 0.006944444445 Combine like terms: -0.006944444445 + 0.006944444445 = 0.000000000000 0.000000000000 + x = 0.23580454 + 0.006944444445 x = 0.23580454 + 0.006944444445 Combine like terms: 0.23580454 + 0.006944444445 = 0.242748984445 x = 0.242748984445 Simplifying x = 0.242748984445Subproblem 2
x + -0.006944444445 = -0.23580454 Simplifying x + -0.006944444445 = -0.23580454 Reorder the terms: -0.006944444445 + x = -0.23580454 Solving -0.006944444445 + x = -0.23580454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006944444445' to each side of the equation. -0.006944444445 + 0.006944444445 + x = -0.23580454 + 0.006944444445 Combine like terms: -0.006944444445 + 0.006944444445 = 0.000000000000 0.000000000000 + x = -0.23580454 + 0.006944444445 x = -0.23580454 + 0.006944444445 Combine like terms: -0.23580454 + 0.006944444445 = -0.228860095555 x = -0.228860095555 Simplifying x = -0.228860095555Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.242748984445, -0.228860095555}
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