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Simplifying x2 + -3.79x + -17.3 = 3.57 Reorder the terms: -17.3 + -3.79x + x2 = 3.57 Solving -17.3 + -3.79x + x2 = 3.57 Solving for variable 'x'. Reorder the terms: -17.3 + -3.57 + -3.79x + x2 = 3.57 + -3.57 Combine like terms: -17.3 + -3.57 = -20.87 -20.87 + -3.79x + x2 = 3.57 + -3.57 Combine like terms: 3.57 + -3.57 = 0.00 -20.87 + -3.79x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '20.87' to each side of the equation. -20.87 + -3.79x + 20.87 + x2 = 0.00 + 20.87 Reorder the terms: -20.87 + 20.87 + -3.79x + x2 = 0.00 + 20.87 Combine like terms: -20.87 + 20.87 = 0.00 0.00 + -3.79x + x2 = 0.00 + 20.87 -3.79x + x2 = 0.00 + 20.87 Combine like terms: 0.00 + 20.87 = 20.87 -3.79x + x2 = 20.87 The x term is -3.79x. Take half its coefficient (-1.895). Square it (3.591025) and add it to both sides. Add '3.591025' to each side of the equation. -3.79x + 3.591025 + x2 = 20.87 + 3.591025 Reorder the terms: 3.591025 + -3.79x + x2 = 20.87 + 3.591025 Combine like terms: 20.87 + 3.591025 = 24.461025 3.591025 + -3.79x + x2 = 24.461025 Factor a perfect square on the left side: (x + -1.895)(x + -1.895) = 24.461025 Calculate the square root of the right side: 4.945808832 Break this problem into two subproblems by setting (x + -1.895) equal to 4.945808832 and -4.945808832.Subproblem 1
x + -1.895 = 4.945808832 Simplifying x + -1.895 = 4.945808832 Reorder the terms: -1.895 + x = 4.945808832 Solving -1.895 + x = 4.945808832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.895' to each side of the equation. -1.895 + 1.895 + x = 4.945808832 + 1.895 Combine like terms: -1.895 + 1.895 = 0.000 0.000 + x = 4.945808832 + 1.895 x = 4.945808832 + 1.895 Combine like terms: 4.945808832 + 1.895 = 6.840808832 x = 6.840808832 Simplifying x = 6.840808832Subproblem 2
x + -1.895 = -4.945808832 Simplifying x + -1.895 = -4.945808832 Reorder the terms: -1.895 + x = -4.945808832 Solving -1.895 + x = -4.945808832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.895' to each side of the equation. -1.895 + 1.895 + x = -4.945808832 + 1.895 Combine like terms: -1.895 + 1.895 = 0.000 0.000 + x = -4.945808832 + 1.895 x = -4.945808832 + 1.895 Combine like terms: -4.945808832 + 1.895 = -3.050808832 x = -3.050808832 Simplifying x = -3.050808832Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.840808832, -3.050808832}
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