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Simplifying 0 = 0.75x2 + -3.4x + 1.92 Reorder the terms: 0 = 1.92 + -3.4x + 0.75x2 Solving 0 = 1.92 + -3.4x + 0.75x2 Solving for variable 'x'. Combine like terms: 0 + -1.92 = -1.92 -1.92 + 3.4x + -0.75x2 = 1.92 + -3.4x + 0.75x2 + -1.92 + 3.4x + -0.75x2 Reorder the terms: -1.92 + 3.4x + -0.75x2 = 1.92 + -1.92 + -3.4x + 3.4x + 0.75x2 + -0.75x2 Combine like terms: 1.92 + -1.92 = 0.00 -1.92 + 3.4x + -0.75x2 = 0.00 + -3.4x + 3.4x + 0.75x2 + -0.75x2 -1.92 + 3.4x + -0.75x2 = -3.4x + 3.4x + 0.75x2 + -0.75x2 Combine like terms: -3.4x + 3.4x = 0.0 -1.92 + 3.4x + -0.75x2 = 0.0 + 0.75x2 + -0.75x2 -1.92 + 3.4x + -0.75x2 = 0.75x2 + -0.75x2 Combine like terms: 0.75x2 + -0.75x2 = 0.00 -1.92 + 3.4x + -0.75x2 = 0.00 Begin completing the square. Divide all terms by -0.75 the coefficient of the squared term: Divide each side by '-0.75'. 2.56 + -4.533333333x + x2 = 0 Move the constant term to the right: Add '-2.56' to each side of the equation. 2.56 + -4.533333333x + -2.56 + x2 = 0 + -2.56 Reorder the terms: 2.56 + -2.56 + -4.533333333x + x2 = 0 + -2.56 Combine like terms: 2.56 + -2.56 = 0.00 0.00 + -4.533333333x + x2 = 0 + -2.56 -4.533333333x + x2 = 0 + -2.56 Combine like terms: 0 + -2.56 = -2.56 -4.533333333x + x2 = -2.56 The x term is -4.533333333x. Take half its coefficient (-2.266666667). Square it (5.137777779) and add it to both sides. Add '5.137777779' to each side of the equation. -4.533333333x + 5.137777779 + x2 = -2.56 + 5.137777779 Reorder the terms: 5.137777779 + -4.533333333x + x2 = -2.56 + 5.137777779 Combine like terms: -2.56 + 5.137777779 = 2.577777779 5.137777779 + -4.533333333x + x2 = 2.577777779 Factor a perfect square on the left side: (x + -2.266666667)(x + -2.266666667) = 2.577777779 Calculate the square root of the right side: 1.605545944 Break this problem into two subproblems by setting (x + -2.266666667) equal to 1.605545944 and -1.605545944.Subproblem 1
x + -2.266666667 = 1.605545944 Simplifying x + -2.266666667 = 1.605545944 Reorder the terms: -2.266666667 + x = 1.605545944 Solving -2.266666667 + x = 1.605545944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.266666667' to each side of the equation. -2.266666667 + 2.266666667 + x = 1.605545944 + 2.266666667 Combine like terms: -2.266666667 + 2.266666667 = 0.000000000 0.000000000 + x = 1.605545944 + 2.266666667 x = 1.605545944 + 2.266666667 Combine like terms: 1.605545944 + 2.266666667 = 3.872212611 x = 3.872212611 Simplifying x = 3.872212611Subproblem 2
x + -2.266666667 = -1.605545944 Simplifying x + -2.266666667 = -1.605545944 Reorder the terms: -2.266666667 + x = -1.605545944 Solving -2.266666667 + x = -1.605545944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.266666667' to each side of the equation. -2.266666667 + 2.266666667 + x = -1.605545944 + 2.266666667 Combine like terms: -2.266666667 + 2.266666667 = 0.000000000 0.000000000 + x = -1.605545944 + 2.266666667 x = -1.605545944 + 2.266666667 Combine like terms: -1.605545944 + 2.266666667 = 0.661120723 x = 0.661120723 Simplifying x = 0.661120723Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.872212611, 0.661120723}
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