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Simplifying 0.006x2 + -0.06x + 0.14 = 0 Reorder the terms: 0.14 + -0.06x + 0.006x2 = 0 Solving 0.14 + -0.06x + 0.006x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.006 the coefficient of the squared term: Divide each side by '0.006'. 23.33333333 + -10x + x2 = 0 Move the constant term to the right: Add '-23.33333333' to each side of the equation. 23.33333333 + -10x + -23.33333333 + x2 = 0 + -23.33333333 Reorder the terms: 23.33333333 + -23.33333333 + -10x + x2 = 0 + -23.33333333 Combine like terms: 23.33333333 + -23.33333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + -23.33333333 -10x + x2 = 0 + -23.33333333 Combine like terms: 0 + -23.33333333 = -23.33333333 -10x + x2 = -23.33333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -23.33333333 + 25 Reorder the terms: 25 + -10x + x2 = -23.33333333 + 25 Combine like terms: -23.33333333 + 25 = 1.66666667 25 + -10x + x2 = 1.66666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 1.66666667 Calculate the square root of the right side: 1.29099445 Break this problem into two subproblems by setting (x + -5) equal to 1.29099445 and -1.29099445.Subproblem 1
x + -5 = 1.29099445 Simplifying x + -5 = 1.29099445 Reorder the terms: -5 + x = 1.29099445 Solving -5 + x = 1.29099445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1.29099445 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.29099445 + 5 x = 1.29099445 + 5 Combine like terms: 1.29099445 + 5 = 6.29099445 x = 6.29099445 Simplifying x = 6.29099445Subproblem 2
x + -5 = -1.29099445 Simplifying x + -5 = -1.29099445 Reorder the terms: -5 + x = -1.29099445 Solving -5 + x = -1.29099445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1.29099445 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.29099445 + 5 x = -1.29099445 + 5 Combine like terms: -1.29099445 + 5 = 3.70900555 x = 3.70900555 Simplifying x = 3.70900555Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.29099445, 3.70900555}
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