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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 = 0.605775034 2.205775034 + -2.97037037x + x2 = 0.605775034 Factor a perfect square on the left side: (x + -1.485185185)(x + -1.485185185) = 0.605775034 Calculate the square root of the right side: 0.778315511 Break this problem into two subproblems by setting (x + -1.485185185) equal to 0.778315511 and -0.778315511.Subproblem 1
x + -1.485185185 = 0.778315511 Simplifying x + -1.485185185 = 0.778315511 Reorder the terms: -1.485185185 + x = 0.778315511 Solving -1.485185185 + x = 0.778315511 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 = 0.778315511 + 1.485185185 Combine like terms: -1.485185185 + 1.485185185 = 0.000000000 0.000000000 + x = 0.778315511 + 1.485185185 x = 0.778315511 + 1.485185185 Combine like terms: 0.778315511 + 1.485185185 = 2.263500696 x = 2.263500696 Simplifying x = 2.263500696Subproblem 2
x + -1.485185185 = -0.778315511 Simplifying x + -1.485185185 = -0.778315511 Reorder the terms: -1.485185185 + x = -0.778315511 Solving -1.485185185 + x = -0.778315511 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 = -0.778315511 + 1.485185185 Combine like terms: -1.485185185 + 1.485185185 = 0.000000000 0.000000000 + x = -0.778315511 + 1.485185185 x = -0.778315511 + 1.485185185 Combine like terms: -0.778315511 + 1.485185185 = 0.706869674 x = 0.706869674 Simplifying x = 0.706869674Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.263500696, 0.706869674}
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