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Simplifying 17x2 + 16x + -4 = 0 Reorder the terms: -4 + 16x + 17x2 = 0 Solving -4 + 16x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.2352941176 + 0.9411764706x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + 0.9411764706x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + 0.9411764706x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + 0.9411764706x + x2 = 0 + 0.2352941176 0.9411764706x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 0.9411764706x + x2 = 0.2352941176 The x term is 0.9411764706x. Take half its coefficient (0.4705882353). Square it (0.2214532872) and add it to both sides. Add '0.2214532872' to each side of the equation. 0.9411764706x + 0.2214532872 + x2 = 0.2352941176 + 0.2214532872 Reorder the terms: 0.2214532872 + 0.9411764706x + x2 = 0.2352941176 + 0.2214532872 Combine like terms: 0.2352941176 + 0.2214532872 = 0.4567474048 0.2214532872 + 0.9411764706x + x2 = 0.4567474048 Factor a perfect square on the left side: (x + 0.4705882353)(x + 0.4705882353) = 0.4567474048 Calculate the square root of the right side: 0.6758309 Break this problem into two subproblems by setting (x + 0.4705882353) equal to 0.6758309 and -0.6758309.Subproblem 1
x + 0.4705882353 = 0.6758309 Simplifying x + 0.4705882353 = 0.6758309 Reorder the terms: 0.4705882353 + x = 0.6758309 Solving 0.4705882353 + x = 0.6758309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4705882353' to each side of the equation. 0.4705882353 + -0.4705882353 + x = 0.6758309 + -0.4705882353 Combine like terms: 0.4705882353 + -0.4705882353 = 0.0000000000 0.0000000000 + x = 0.6758309 + -0.4705882353 x = 0.6758309 + -0.4705882353 Combine like terms: 0.6758309 + -0.4705882353 = 0.2052426647 x = 0.2052426647 Simplifying x = 0.2052426647Subproblem 2
x + 0.4705882353 = -0.6758309 Simplifying x + 0.4705882353 = -0.6758309 Reorder the terms: 0.4705882353 + x = -0.6758309 Solving 0.4705882353 + x = -0.6758309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4705882353' to each side of the equation. 0.4705882353 + -0.4705882353 + x = -0.6758309 + -0.4705882353 Combine like terms: 0.4705882353 + -0.4705882353 = 0.0000000000 0.0000000000 + x = -0.6758309 + -0.4705882353 x = -0.6758309 + -0.4705882353 Combine like terms: -0.6758309 + -0.4705882353 = -1.1464191353 x = -1.1464191353 Simplifying x = -1.1464191353Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2052426647, -1.1464191353}
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