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Simplifying 0.2x2 + -0.2x + 0.659 = x Reorder the terms: 0.659 + -0.2x + 0.2x2 = x Solving 0.659 + -0.2x + 0.2x2 = x Solving for variable 'x'. Reorder the terms: 0.659 + -0.2x + -1x + 0.2x2 = x + -1x Combine like terms: -0.2x + -1x = -1.2x 0.659 + -1.2x + 0.2x2 = x + -1x Combine like terms: x + -1x = 0 0.659 + -1.2x + 0.2x2 = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 3.295 + -6x + x2 = 0 Move the constant term to the right: Add '-3.295' to each side of the equation. 3.295 + -6x + -3.295 + x2 = 0 + -3.295 Reorder the terms: 3.295 + -3.295 + -6x + x2 = 0 + -3.295 Combine like terms: 3.295 + -3.295 = 0.000 0.000 + -6x + x2 = 0 + -3.295 -6x + x2 = 0 + -3.295 Combine like terms: 0 + -3.295 = -3.295 -6x + x2 = -3.295 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -3.295 + 9 Reorder the terms: 9 + -6x + x2 = -3.295 + 9 Combine like terms: -3.295 + 9 = 5.705 9 + -6x + x2 = 5.705 Factor a perfect square on the left side: (x + -3)(x + -3) = 5.705 Calculate the square root of the right side: 2.388514182 Break this problem into two subproblems by setting (x + -3) equal to 2.388514182 and -2.388514182.Subproblem 1
x + -3 = 2.388514182 Simplifying x + -3 = 2.388514182 Reorder the terms: -3 + x = 2.388514182 Solving -3 + x = 2.388514182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.388514182 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.388514182 + 3 x = 2.388514182 + 3 Combine like terms: 2.388514182 + 3 = 5.388514182 x = 5.388514182 Simplifying x = 5.388514182Subproblem 2
x + -3 = -2.388514182 Simplifying x + -3 = -2.388514182 Reorder the terms: -3 + x = -2.388514182 Solving -3 + x = -2.388514182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.388514182 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.388514182 + 3 x = -2.388514182 + 3 Combine like terms: -2.388514182 + 3 = 0.611485818 x = 0.611485818 Simplifying x = 0.611485818Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.388514182, 0.611485818}
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