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Simplifying -3x2 + 10x + 0.6 = 0 Reorder the terms: 0.6 + 10x + -3x2 = 0 Solving 0.6 + 10x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.2 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -3.333333333x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -3.333333333x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -3.333333333x + x2 = 0 + 0.2 -3.333333333x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -3.333333333x + x2 = 0.2 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 0.2 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 0.2 + 2.777777779 Combine like terms: 0.2 + 2.777777779 = 2.977777779 2.777777779 + -3.333333333x + x2 = 2.977777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 2.977777779 Calculate the square root of the right side: 1.725623881 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.725623881 and -1.725623881.Subproblem 1
x + -1.666666667 = 1.725623881 Simplifying x + -1.666666667 = 1.725623881 Reorder the terms: -1.666666667 + x = 1.725623881 Solving -1.666666667 + x = 1.725623881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.725623881 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.725623881 + 1.666666667 x = 1.725623881 + 1.666666667 Combine like terms: 1.725623881 + 1.666666667 = 3.392290548 x = 3.392290548 Simplifying x = 3.392290548Subproblem 2
x + -1.666666667 = -1.725623881 Simplifying x + -1.666666667 = -1.725623881 Reorder the terms: -1.666666667 + x = -1.725623881 Solving -1.666666667 + x = -1.725623881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.725623881 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.725623881 + 1.666666667 x = -1.725623881 + 1.666666667 Combine like terms: -1.725623881 + 1.666666667 = -0.058957214 x = -0.058957214 Simplifying x = -0.058957214Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.392290548, -0.058957214}
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