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Simplifying 0.55x2 + -3x + -0.81 = 0 Reorder the terms: -0.81 + -3x + 0.55x2 = 0 Solving -0.81 + -3x + 0.55x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.55 the coefficient of the squared term: Divide each side by '0.55'. -1.472727273 + -5.454545455x + x2 = 0 Move the constant term to the right: Add '1.472727273' to each side of the equation. -1.472727273 + -5.454545455x + 1.472727273 + x2 = 0 + 1.472727273 Reorder the terms: -1.472727273 + 1.472727273 + -5.454545455x + x2 = 0 + 1.472727273 Combine like terms: -1.472727273 + 1.472727273 = 0.000000000 0.000000000 + -5.454545455x + x2 = 0 + 1.472727273 -5.454545455x + x2 = 0 + 1.472727273 Combine like terms: 0 + 1.472727273 = 1.472727273 -5.454545455x + x2 = 1.472727273 The x term is -5.454545455x. Take half its coefficient (-2.727272728). Square it (7.438016533) and add it to both sides. Add '7.438016533' to each side of the equation. -5.454545455x + 7.438016533 + x2 = 1.472727273 + 7.438016533 Reorder the terms: 7.438016533 + -5.454545455x + x2 = 1.472727273 + 7.438016533 Combine like terms: 1.472727273 + 7.438016533 = 8.910743806 7.438016533 + -5.454545455x + x2 = 8.910743806 Factor a perfect square on the left side: (x + -2.727272728)(x + -2.727272728) = 8.910743806 Calculate the square root of the right side: 2.985086901 Break this problem into two subproblems by setting (x + -2.727272728) equal to 2.985086901 and -2.985086901.Subproblem 1
x + -2.727272728 = 2.985086901 Simplifying x + -2.727272728 = 2.985086901 Reorder the terms: -2.727272728 + x = 2.985086901 Solving -2.727272728 + x = 2.985086901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.727272728' to each side of the equation. -2.727272728 + 2.727272728 + x = 2.985086901 + 2.727272728 Combine like terms: -2.727272728 + 2.727272728 = 0.000000000 0.000000000 + x = 2.985086901 + 2.727272728 x = 2.985086901 + 2.727272728 Combine like terms: 2.985086901 + 2.727272728 = 5.712359629 x = 5.712359629 Simplifying x = 5.712359629Subproblem 2
x + -2.727272728 = -2.985086901 Simplifying x + -2.727272728 = -2.985086901 Reorder the terms: -2.727272728 + x = -2.985086901 Solving -2.727272728 + x = -2.985086901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.727272728' to each side of the equation. -2.727272728 + 2.727272728 + x = -2.985086901 + 2.727272728 Combine like terms: -2.727272728 + 2.727272728 = 0.000000000 0.000000000 + x = -2.985086901 + 2.727272728 x = -2.985086901 + 2.727272728 Combine like terms: -2.985086901 + 2.727272728 = -0.257814173 x = -0.257814173 Simplifying x = -0.257814173Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.712359629, -0.257814173}
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