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Simplifying 27x2 + -28x + -1 = 0 Reorder the terms: -1 + -28x + 27x2 = 0 Solving -1 + -28x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.03703703704 + -1.037037037x + x2 = 0 Move the constant term to the right: Add '0.03703703704' to each side of the equation. -0.03703703704 + -1.037037037x + 0.03703703704 + x2 = 0 + 0.03703703704 Reorder the terms: -0.03703703704 + 0.03703703704 + -1.037037037x + x2 = 0 + 0.03703703704 Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000 0.00000000000 + -1.037037037x + x2 = 0 + 0.03703703704 -1.037037037x + x2 = 0 + 0.03703703704 Combine like terms: 0 + 0.03703703704 = 0.03703703704 -1.037037037x + x2 = 0.03703703704 The x term is -1.037037037x. Take half its coefficient (-0.5185185185). Square it (0.2688614540) and add it to both sides. Add '0.2688614540' to each side of the equation. -1.037037037x + 0.2688614540 + x2 = 0.03703703704 + 0.2688614540 Reorder the terms: 0.2688614540 + -1.037037037x + x2 = 0.03703703704 + 0.2688614540 Combine like terms: 0.03703703704 + 0.2688614540 = 0.30589849104 0.2688614540 + -1.037037037x + x2 = 0.30589849104 Factor a perfect square on the left side: (x + -0.5185185185)(x + -0.5185185185) = 0.30589849104 Calculate the square root of the right side: 0.553080908 Break this problem into two subproblems by setting (x + -0.5185185185) equal to 0.553080908 and -0.553080908.Subproblem 1
x + -0.5185185185 = 0.553080908 Simplifying x + -0.5185185185 = 0.553080908 Reorder the terms: -0.5185185185 + x = 0.553080908 Solving -0.5185185185 + x = 0.553080908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5185185185' to each side of the equation. -0.5185185185 + 0.5185185185 + x = 0.553080908 + 0.5185185185 Combine like terms: -0.5185185185 + 0.5185185185 = 0.0000000000 0.0000000000 + x = 0.553080908 + 0.5185185185 x = 0.553080908 + 0.5185185185 Combine like terms: 0.553080908 + 0.5185185185 = 1.0715994265 x = 1.0715994265 Simplifying x = 1.0715994265Subproblem 2
x + -0.5185185185 = -0.553080908 Simplifying x + -0.5185185185 = -0.553080908 Reorder the terms: -0.5185185185 + x = -0.553080908 Solving -0.5185185185 + x = -0.553080908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5185185185' to each side of the equation. -0.5185185185 + 0.5185185185 + x = -0.553080908 + 0.5185185185 Combine like terms: -0.5185185185 + 0.5185185185 = 0.0000000000 0.0000000000 + x = -0.553080908 + 0.5185185185 x = -0.553080908 + 0.5185185185 Combine like terms: -0.553080908 + 0.5185185185 = -0.0345623895 x = -0.0345623895 Simplifying x = -0.0345623895Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0715994265, -0.0345623895}
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