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Simplifying 81x2 + -35x + -3 = 0 Reorder the terms: -3 + -35x + 81x2 = 0 Solving -3 + -35x + 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'. -0.03703703704 + -0.4320987654x + x2 = 0 Move the constant term to the right: Add '0.03703703704' to each side of the equation. -0.03703703704 + -0.4320987654x + 0.03703703704 + x2 = 0 + 0.03703703704 Reorder the terms: -0.03703703704 + 0.03703703704 + -0.4320987654x + x2 = 0 + 0.03703703704 Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000 0.00000000000 + -0.4320987654x + x2 = 0 + 0.03703703704 -0.4320987654x + x2 = 0 + 0.03703703704 Combine like terms: 0 + 0.03703703704 = 0.03703703704 -0.4320987654x + x2 = 0.03703703704 The x term is -0.4320987654x. Take half its coefficient (-0.2160493827). Square it (0.04667733577) and add it to both sides. Add '0.04667733577' to each side of the equation. -0.4320987654x + 0.04667733577 + x2 = 0.03703703704 + 0.04667733577 Reorder the terms: 0.04667733577 + -0.4320987654x + x2 = 0.03703703704 + 0.04667733577 Combine like terms: 0.03703703704 + 0.04667733577 = 0.08371437281 0.04667733577 + -0.4320987654x + x2 = 0.08371437281 Factor a perfect square on the left side: (x + -0.2160493827)(x + -0.2160493827) = 0.08371437281 Calculate the square root of the right side: 0.289334362 Break this problem into two subproblems by setting (x + -0.2160493827) equal to 0.289334362 and -0.289334362.Subproblem 1
x + -0.2160493827 = 0.289334362 Simplifying x + -0.2160493827 = 0.289334362 Reorder the terms: -0.2160493827 + x = 0.289334362 Solving -0.2160493827 + x = 0.289334362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2160493827' to each side of the equation. -0.2160493827 + 0.2160493827 + x = 0.289334362 + 0.2160493827 Combine like terms: -0.2160493827 + 0.2160493827 = 0.0000000000 0.0000000000 + x = 0.289334362 + 0.2160493827 x = 0.289334362 + 0.2160493827 Combine like terms: 0.289334362 + 0.2160493827 = 0.5053837447 x = 0.5053837447 Simplifying x = 0.5053837447Subproblem 2
x + -0.2160493827 = -0.289334362 Simplifying x + -0.2160493827 = -0.289334362 Reorder the terms: -0.2160493827 + x = -0.289334362 Solving -0.2160493827 + x = -0.289334362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2160493827' to each side of the equation. -0.2160493827 + 0.2160493827 + x = -0.289334362 + 0.2160493827 Combine like terms: -0.2160493827 + 0.2160493827 = 0.0000000000 0.0000000000 + x = -0.289334362 + 0.2160493827 x = -0.289334362 + 0.2160493827 Combine like terms: -0.289334362 + 0.2160493827 = -0.0732849793 x = -0.0732849793 Simplifying x = -0.0732849793Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5053837447, -0.0732849793}
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