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Simplifying -0.1666666667x2 + 1.5x + -3 = 0 Reorder the terms: -3 + 1.5x + -0.1666666667x2 = 0 Solving -3 + 1.5x + -0.1666666667x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1666666667 the coefficient of the squared term: Divide each side by '-0.1666666667'. 18 + -8.999999998x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -8.999999998x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -8.999999998x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -8.999999998x + x2 = 0 + -18 -8.999999998x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -8.999999998x + x2 = -18 The x term is -8.999999998x. Take half its coefficient (-4.499999999). Square it (20.24999999) and add it to both sides. Add '20.24999999' to each side of the equation. -8.999999998x + 20.24999999 + x2 = -18 + 20.24999999 Reorder the terms: 20.24999999 + -8.999999998x + x2 = -18 + 20.24999999 Combine like terms: -18 + 20.24999999 = 2.24999999 20.24999999 + -8.999999998x + x2 = 2.24999999 Factor a perfect square on the left side: (x + -4.499999999)(x + -4.499999999) = 2.24999999 Calculate the square root of the right side: 1.499999997 Break this problem into two subproblems by setting (x + -4.499999999) equal to 1.499999997 and -1.499999997.Subproblem 1
x + -4.499999999 = 1.499999997 Simplifying x + -4.499999999 = 1.499999997 Reorder the terms: -4.499999999 + x = 1.499999997 Solving -4.499999999 + x = 1.499999997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.499999999' to each side of the equation. -4.499999999 + 4.499999999 + x = 1.499999997 + 4.499999999 Combine like terms: -4.499999999 + 4.499999999 = 0.000000000 0.000000000 + x = 1.499999997 + 4.499999999 x = 1.499999997 + 4.499999999 Combine like terms: 1.499999997 + 4.499999999 = 5.999999996 x = 5.999999996 Simplifying x = 5.999999996Subproblem 2
x + -4.499999999 = -1.499999997 Simplifying x + -4.499999999 = -1.499999997 Reorder the terms: -4.499999999 + x = -1.499999997 Solving -4.499999999 + x = -1.499999997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.499999999' to each side of the equation. -4.499999999 + 4.499999999 + x = -1.499999997 + 4.499999999 Combine like terms: -4.499999999 + 4.499999999 = 0.000000000 0.000000000 + x = -1.499999997 + 4.499999999 x = -1.499999997 + 4.499999999 Combine like terms: -1.499999997 + 4.499999999 = 3.000000002 x = 3.000000002 Simplifying x = 3.000000002Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.999999996, 3.000000002}
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