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Simplifying 13x2 + 8.82x + -81 = 0 Reorder the terms: -81 + 8.82x + 13x2 = 0 Solving -81 + 8.82x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -6.230769231 + 0.6784615385x + x2 = 0 Move the constant term to the right: Add '6.230769231' to each side of the equation. -6.230769231 + 0.6784615385x + 6.230769231 + x2 = 0 + 6.230769231 Reorder the terms: -6.230769231 + 6.230769231 + 0.6784615385x + x2 = 0 + 6.230769231 Combine like terms: -6.230769231 + 6.230769231 = 0.000000000 0.000000000 + 0.6784615385x + x2 = 0 + 6.230769231 0.6784615385x + x2 = 0 + 6.230769231 Combine like terms: 0 + 6.230769231 = 6.230769231 0.6784615385x + x2 = 6.230769231 The x term is 0.6784615385x. Take half its coefficient (0.3392307693). Square it (0.1150775148) and add it to both sides. Add '0.1150775148' to each side of the equation. 0.6784615385x + 0.1150775148 + x2 = 6.230769231 + 0.1150775148 Reorder the terms: 0.1150775148 + 0.6784615385x + x2 = 6.230769231 + 0.1150775148 Combine like terms: 6.230769231 + 0.1150775148 = 6.3458467458 0.1150775148 + 0.6784615385x + x2 = 6.3458467458 Factor a perfect square on the left side: (x + 0.3392307693)(x + 0.3392307693) = 6.3458467458 Calculate the square root of the right side: 2.519096415 Break this problem into two subproblems by setting (x + 0.3392307693) equal to 2.519096415 and -2.519096415.Subproblem 1
x + 0.3392307693 = 2.519096415 Simplifying x + 0.3392307693 = 2.519096415 Reorder the terms: 0.3392307693 + x = 2.519096415 Solving 0.3392307693 + x = 2.519096415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3392307693' to each side of the equation. 0.3392307693 + -0.3392307693 + x = 2.519096415 + -0.3392307693 Combine like terms: 0.3392307693 + -0.3392307693 = 0.0000000000 0.0000000000 + x = 2.519096415 + -0.3392307693 x = 2.519096415 + -0.3392307693 Combine like terms: 2.519096415 + -0.3392307693 = 2.1798656457 x = 2.1798656457 Simplifying x = 2.1798656457Subproblem 2
x + 0.3392307693 = -2.519096415 Simplifying x + 0.3392307693 = -2.519096415 Reorder the terms: 0.3392307693 + x = -2.519096415 Solving 0.3392307693 + x = -2.519096415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3392307693' to each side of the equation. 0.3392307693 + -0.3392307693 + x = -2.519096415 + -0.3392307693 Combine like terms: 0.3392307693 + -0.3392307693 = 0.0000000000 0.0000000000 + x = -2.519096415 + -0.3392307693 x = -2.519096415 + -0.3392307693 Combine like terms: -2.519096415 + -0.3392307693 = -2.8583271843 x = -2.8583271843 Simplifying x = -2.8583271843Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1798656457, -2.8583271843}
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