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Simplifying 4.9x2 + 5x + -0.1 = 0 Reorder the terms: -0.1 + 5x + 4.9x2 = 0 Solving -0.1 + 5x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.02040816327 + 1.020408163x + x2 = 0 Move the constant term to the right: Add '0.02040816327' to each side of the equation. -0.02040816327 + 1.020408163x + 0.02040816327 + x2 = 0 + 0.02040816327 Reorder the terms: -0.02040816327 + 0.02040816327 + 1.020408163x + x2 = 0 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + 1.020408163x + x2 = 0 + 0.02040816327 1.020408163x + x2 = 0 + 0.02040816327 Combine like terms: 0 + 0.02040816327 = 0.02040816327 1.020408163x + x2 = 0.02040816327 The x term is 1.020408163x. Take half its coefficient (0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. 1.020408163x + 0.2603082048 + x2 = 0.02040816327 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163x + x2 = 0.02040816327 + 0.2603082048 Combine like terms: 0.02040816327 + 0.2603082048 = 0.28071636807 0.2603082048 + 1.020408163x + x2 = 0.28071636807 Factor a perfect square on the left side: (x + 0.5102040815)(x + 0.5102040815) = 0.28071636807 Calculate the square root of the right side: 0.529826734 Break this problem into two subproblems by setting (x + 0.5102040815) equal to 0.529826734 and -0.529826734.Subproblem 1
x + 0.5102040815 = 0.529826734 Simplifying x + 0.5102040815 = 0.529826734 Reorder the terms: 0.5102040815 + x = 0.529826734 Solving 0.5102040815 + x = 0.529826734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + x = 0.529826734 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = 0.529826734 + -0.5102040815 x = 0.529826734 + -0.5102040815 Combine like terms: 0.529826734 + -0.5102040815 = 0.0196226525 x = 0.0196226525 Simplifying x = 0.0196226525Subproblem 2
x + 0.5102040815 = -0.529826734 Simplifying x + 0.5102040815 = -0.529826734 Reorder the terms: 0.5102040815 + x = -0.529826734 Solving 0.5102040815 + x = -0.529826734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + x = -0.529826734 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = -0.529826734 + -0.5102040815 x = -0.529826734 + -0.5102040815 Combine like terms: -0.529826734 + -0.5102040815 = -1.0400308155 x = -1.0400308155 Simplifying x = -1.0400308155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0196226525, -1.0400308155}
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