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Simplifying 81x2 + -13x + -55 = 0 Reorder the terms: -55 + -13x + 81x2 = 0 Solving -55 + -13x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.6790123457 + -0.1604938272x + x2 = 0 Move the constant term to the right: Add '0.6790123457' to each side of the equation. -0.6790123457 + -0.1604938272x + 0.6790123457 + x2 = 0 + 0.6790123457 Reorder the terms: -0.6790123457 + 0.6790123457 + -0.1604938272x + x2 = 0 + 0.6790123457 Combine like terms: -0.6790123457 + 0.6790123457 = 0.0000000000 0.0000000000 + -0.1604938272x + x2 = 0 + 0.6790123457 -0.1604938272x + x2 = 0 + 0.6790123457 Combine like terms: 0 + 0.6790123457 = 0.6790123457 -0.1604938272x + x2 = 0.6790123457 The x term is -0.1604938272x. Take half its coefficient (-0.0802469136). Square it (0.006439567142) and add it to both sides. Add '0.006439567142' to each side of the equation. -0.1604938272x + 0.006439567142 + x2 = 0.6790123457 + 0.006439567142 Reorder the terms: 0.006439567142 + -0.1604938272x + x2 = 0.6790123457 + 0.006439567142 Combine like terms: 0.6790123457 + 0.006439567142 = 0.685451912842 0.006439567142 + -0.1604938272x + x2 = 0.685451912842 Factor a perfect square on the left side: (x + -0.0802469136)(x + -0.0802469136) = 0.685451912842 Calculate the square root of the right side: 0.827920233 Break this problem into two subproblems by setting (x + -0.0802469136) equal to 0.827920233 and -0.827920233.Subproblem 1
x + -0.0802469136 = 0.827920233 Simplifying x + -0.0802469136 = 0.827920233 Reorder the terms: -0.0802469136 + x = 0.827920233 Solving -0.0802469136 + x = 0.827920233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0802469136' to each side of the equation. -0.0802469136 + 0.0802469136 + x = 0.827920233 + 0.0802469136 Combine like terms: -0.0802469136 + 0.0802469136 = 0.0000000000 0.0000000000 + x = 0.827920233 + 0.0802469136 x = 0.827920233 + 0.0802469136 Combine like terms: 0.827920233 + 0.0802469136 = 0.9081671466 x = 0.9081671466 Simplifying x = 0.9081671466Subproblem 2
x + -0.0802469136 = -0.827920233 Simplifying x + -0.0802469136 = -0.827920233 Reorder the terms: -0.0802469136 + x = -0.827920233 Solving -0.0802469136 + x = -0.827920233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0802469136' to each side of the equation. -0.0802469136 + 0.0802469136 + x = -0.827920233 + 0.0802469136 Combine like terms: -0.0802469136 + 0.0802469136 = 0.0000000000 0.0000000000 + x = -0.827920233 + 0.0802469136 x = -0.827920233 + 0.0802469136 Combine like terms: -0.827920233 + 0.0802469136 = -0.7476733194 x = -0.7476733194 Simplifying x = -0.7476733194Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9081671466, -0.7476733194}
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