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Simplifying -2.7x2 + -8.02x + 4.32 = 0 Reorder the terms: 4.32 + -8.02x + -2.7x2 = 0 Solving 4.32 + -8.02x + -2.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. -1.6 + 2.97037037x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 2.97037037x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 2.97037037x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 2.97037037x + x2 = 0 + 1.6 2.97037037x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 2.97037037x + x2 = 1.6 The x term is 2.97037037x. Take half its coefficient (1.485185185). Square it (2.205775034) and add it to both sides. Add '2.205775034' to each side of the equation. 2.97037037x + 2.205775034 + x2 = 1.6 + 2.205775034 Reorder the terms: 2.205775034 + 2.97037037x + x2 = 1.6 + 2.205775034 Combine like terms: 1.6 + 2.205775034 = 3.805775034 2.205775034 + 2.97037037x + x2 = 3.805775034 Factor a perfect square on the left side: (x + 1.485185185)(x + 1.485185185) = 3.805775034 Calculate the square root of the right side: 1.950839572 Break this problem into two subproblems by setting (x + 1.485185185) equal to 1.950839572 and -1.950839572.Subproblem 1
x + 1.485185185 = 1.950839572 Simplifying x + 1.485185185 = 1.950839572 Reorder the terms: 1.485185185 + x = 1.950839572 Solving 1.485185185 + x = 1.950839572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.485185185' to each side of the equation. 1.485185185 + -1.485185185 + x = 1.950839572 + -1.485185185 Combine like terms: 1.485185185 + -1.485185185 = 0.000000000 0.000000000 + x = 1.950839572 + -1.485185185 x = 1.950839572 + -1.485185185 Combine like terms: 1.950839572 + -1.485185185 = 0.465654387 x = 0.465654387 Simplifying x = 0.465654387Subproblem 2
x + 1.485185185 = -1.950839572 Simplifying x + 1.485185185 = -1.950839572 Reorder the terms: 1.485185185 + x = -1.950839572 Solving 1.485185185 + x = -1.950839572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.485185185' to each side of the equation. 1.485185185 + -1.485185185 + x = -1.950839572 + -1.485185185 Combine like terms: 1.485185185 + -1.485185185 = 0.000000000 0.000000000 + x = -1.950839572 + -1.485185185 x = -1.950839572 + -1.485185185 Combine like terms: -1.950839572 + -1.485185185 = -3.436024757 x = -3.436024757 Simplifying x = -3.436024757Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.465654387, -3.436024757}
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