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Simplifying 4.9x2 + 5x + -0.06 = 0 Reorder the terms: -0.06 + 5x + 4.9x2 = 0 Solving -0.06 + 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'. -0.01224489796 + 1.020408163x + x2 = 0 Move the constant term to the right: Add '0.01224489796' to each side of the equation. -0.01224489796 + 1.020408163x + 0.01224489796 + x2 = 0 + 0.01224489796 Reorder the terms: -0.01224489796 + 0.01224489796 + 1.020408163x + x2 = 0 + 0.01224489796 Combine like terms: -0.01224489796 + 0.01224489796 = 0.00000000000 0.00000000000 + 1.020408163x + x2 = 0 + 0.01224489796 1.020408163x + x2 = 0 + 0.01224489796 Combine like terms: 0 + 0.01224489796 = 0.01224489796 1.020408163x + x2 = 0.01224489796 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 = 0.01224489796 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163x + x2 = 0.01224489796 + 0.2603082048 Combine like terms: 0.01224489796 + 0.2603082048 = 0.27255310276 0.2603082048 + 1.020408163x + x2 = 0.27255310276 Factor a perfect square on the left side: (x + 0.5102040815)(x + 0.5102040815) = 0.27255310276 Calculate the square root of the right side: 0.522066186 Break this problem into two subproblems by setting (x + 0.5102040815) equal to 0.522066186 and -0.522066186.Subproblem 1
x + 0.5102040815 = 0.522066186 Simplifying x + 0.5102040815 = 0.522066186 Reorder the terms: 0.5102040815 + x = 0.522066186 Solving 0.5102040815 + x = 0.522066186 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 = 0.522066186 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = 0.522066186 + -0.5102040815 x = 0.522066186 + -0.5102040815 Combine like terms: 0.522066186 + -0.5102040815 = 0.0118621045 x = 0.0118621045 Simplifying x = 0.0118621045Subproblem 2
x + 0.5102040815 = -0.522066186 Simplifying x + 0.5102040815 = -0.522066186 Reorder the terms: 0.5102040815 + x = -0.522066186 Solving 0.5102040815 + x = -0.522066186 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 = -0.522066186 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = -0.522066186 + -0.5102040815 x = -0.522066186 + -0.5102040815 Combine like terms: -0.522066186 + -0.5102040815 = -1.0322702675 x = -1.0322702675 Simplifying x = -1.0322702675Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0118621045, -1.0322702675}
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