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Simplifying 2.943x2 + -3.255x + -0.9 = 0 Reorder the terms: -0.9 + -3.255x + 2.943x2 = 0 Solving -0.9 + -3.255x + 2.943x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.943 the coefficient of the squared term: Divide each side by '2.943'. -0.3058103976 + -1.106014271x + x2 = 0 Move the constant term to the right: Add '0.3058103976' to each side of the equation. -0.3058103976 + -1.106014271x + 0.3058103976 + x2 = 0 + 0.3058103976 Reorder the terms: -0.3058103976 + 0.3058103976 + -1.106014271x + x2 = 0 + 0.3058103976 Combine like terms: -0.3058103976 + 0.3058103976 = 0.0000000000 0.0000000000 + -1.106014271x + x2 = 0 + 0.3058103976 -1.106014271x + x2 = 0 + 0.3058103976 Combine like terms: 0 + 0.3058103976 = 0.3058103976 -1.106014271x + x2 = 0.3058103976 The x term is -1.106014271x. Take half its coefficient (-0.5530071355). Square it (0.3058168919) and add it to both sides. Add '0.3058168919' to each side of the equation. -1.106014271x + 0.3058168919 + x2 = 0.3058103976 + 0.3058168919 Reorder the terms: 0.3058168919 + -1.106014271x + x2 = 0.3058103976 + 0.3058168919 Combine like terms: 0.3058103976 + 0.3058168919 = 0.6116272895 0.3058168919 + -1.106014271x + x2 = 0.6116272895 Factor a perfect square on the left side: (x + -0.5530071355)(x + -0.5530071355) = 0.6116272895 Calculate the square root of the right side: 0.782066039 Break this problem into two subproblems by setting (x + -0.5530071355) equal to 0.782066039 and -0.782066039.Subproblem 1
x + -0.5530071355 = 0.782066039 Simplifying x + -0.5530071355 = 0.782066039 Reorder the terms: -0.5530071355 + x = 0.782066039 Solving -0.5530071355 + x = 0.782066039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5530071355' to each side of the equation. -0.5530071355 + 0.5530071355 + x = 0.782066039 + 0.5530071355 Combine like terms: -0.5530071355 + 0.5530071355 = 0.0000000000 0.0000000000 + x = 0.782066039 + 0.5530071355 x = 0.782066039 + 0.5530071355 Combine like terms: 0.782066039 + 0.5530071355 = 1.3350731745 x = 1.3350731745 Simplifying x = 1.3350731745Subproblem 2
x + -0.5530071355 = -0.782066039 Simplifying x + -0.5530071355 = -0.782066039 Reorder the terms: -0.5530071355 + x = -0.782066039 Solving -0.5530071355 + x = -0.782066039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5530071355' to each side of the equation. -0.5530071355 + 0.5530071355 + x = -0.782066039 + 0.5530071355 Combine like terms: -0.5530071355 + 0.5530071355 = 0.0000000000 0.0000000000 + x = -0.782066039 + 0.5530071355 x = -0.782066039 + 0.5530071355 Combine like terms: -0.782066039 + 0.5530071355 = -0.2290589035 x = -0.2290589035 Simplifying x = -0.2290589035Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3350731745, -0.2290589035}
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