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Simplifying 8x2 + -26.83281573x + 9 = 0 Reorder the terms: 9 + -26.83281573x + 8x2 = 0 Solving 9 + -26.83281573x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -3.354101966x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -3.354101966x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -3.354101966x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -3.354101966x + x2 = 0 + -1.125 -3.354101966x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -3.354101966x + x2 = -1.125 The x term is -3.354101966x. Take half its coefficient (-1.677050983). Square it (2.812500000) and add it to both sides. Add '2.812500000' to each side of the equation. -3.354101966x + 2.812500000 + x2 = -1.125 + 2.812500000 Reorder the terms: 2.812500000 + -3.354101966x + x2 = -1.125 + 2.812500000 Combine like terms: -1.125 + 2.812500000 = 1.6875 2.812500000 + -3.354101966x + x2 = 1.6875 Factor a perfect square on the left side: (x + -1.677050983)(x + -1.677050983) = 1.6875 Calculate the square root of the right side: 1.299038106 Break this problem into two subproblems by setting (x + -1.677050983) equal to 1.299038106 and -1.299038106.Subproblem 1
x + -1.677050983 = 1.299038106 Simplifying x + -1.677050983 = 1.299038106 Reorder the terms: -1.677050983 + x = 1.299038106 Solving -1.677050983 + x = 1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.677050983' to each side of the equation. -1.677050983 + 1.677050983 + x = 1.299038106 + 1.677050983 Combine like terms: -1.677050983 + 1.677050983 = 0.000000000 0.000000000 + x = 1.299038106 + 1.677050983 x = 1.299038106 + 1.677050983 Combine like terms: 1.299038106 + 1.677050983 = 2.976089089 x = 2.976089089 Simplifying x = 2.976089089Subproblem 2
x + -1.677050983 = -1.299038106 Simplifying x + -1.677050983 = -1.299038106 Reorder the terms: -1.677050983 + x = -1.299038106 Solving -1.677050983 + x = -1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.677050983' to each side of the equation. -1.677050983 + 1.677050983 + x = -1.299038106 + 1.677050983 Combine like terms: -1.677050983 + 1.677050983 = 0.000000000 0.000000000 + x = -1.299038106 + 1.677050983 x = -1.299038106 + 1.677050983 Combine like terms: -1.299038106 + 1.677050983 = 0.378012877 x = 0.378012877 Simplifying x = 0.378012877Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.976089089, 0.378012877}
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