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Simplifying -0.3x2 + 0.1x = -0.06 Reorder the terms: 0.1x + -0.3x2 = -0.06 Solving 0.1x + -0.3x2 = -0.06 Solving for variable 'x'. Reorder the terms: 0.06 + 0.1x + -0.3x2 = -0.06 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.06 + 0.1x + -0.3x2 = 0.00 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -0.2 + -0.3333333333x + x2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.3333333333x + 0.2 + x2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.3333333333x + x2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.3333333333x + x2 = 0.0 + 0.2 -0.3333333333x + x2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 -0.3333333333x + x2 = 0.2 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.2 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.2 + 0.02777777779 Combine like terms: 0.2 + 0.02777777779 = 0.22777777779 0.02777777779 + -0.3333333333x + x2 = 0.22777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.22777777779 Calculate the square root of the right side: 0.477260702 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.477260702 and -0.477260702.Subproblem 1
x + -0.1666666667 = 0.477260702 Simplifying x + -0.1666666667 = 0.477260702 Reorder the terms: -0.1666666667 + x = 0.477260702 Solving -0.1666666667 + x = 0.477260702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.477260702 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.477260702 + 0.1666666667 x = 0.477260702 + 0.1666666667 Combine like terms: 0.477260702 + 0.1666666667 = 0.6439273687 x = 0.6439273687 Simplifying x = 0.6439273687Subproblem 2
x + -0.1666666667 = -0.477260702 Simplifying x + -0.1666666667 = -0.477260702 Reorder the terms: -0.1666666667 + x = -0.477260702 Solving -0.1666666667 + x = -0.477260702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.477260702 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.477260702 + 0.1666666667 x = -0.477260702 + 0.1666666667 Combine like terms: -0.477260702 + 0.1666666667 = -0.3105940353 x = -0.3105940353 Simplifying x = -0.3105940353Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6439273687, -0.3105940353}
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