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Simplifying 4.9x2 + 4x + 0.7 = 0 Reorder the terms: 0.7 + 4x + 4.9x2 = 0 Solving 0.7 + 4x + 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'. 0.1428571429 + 0.8163265306x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.8163265306x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.8163265306x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.8163265306x + x2 = 0 + -0.1428571429 0.8163265306x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.8163265306x + x2 = -0.1428571429 The x term is 0.8163265306x. Take half its coefficient (0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. 0.8163265306x + 0.1665972511 + x2 = -0.1428571429 + 0.1665972511 Reorder the terms: 0.1665972511 + 0.8163265306x + x2 = -0.1428571429 + 0.1665972511 Combine like terms: -0.1428571429 + 0.1665972511 = 0.0237401082 0.1665972511 + 0.8163265306x + x2 = 0.0237401082 Factor a perfect square on the left side: (x + 0.4081632653)(x + 0.4081632653) = 0.0237401082 Calculate the square root of the right side: 0.154078253 Break this problem into two subproblems by setting (x + 0.4081632653) equal to 0.154078253 and -0.154078253.Subproblem 1
x + 0.4081632653 = 0.154078253 Simplifying x + 0.4081632653 = 0.154078253 Reorder the terms: 0.4081632653 + x = 0.154078253 Solving 0.4081632653 + x = 0.154078253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + x = 0.154078253 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + x = 0.154078253 + -0.4081632653 x = 0.154078253 + -0.4081632653 Combine like terms: 0.154078253 + -0.4081632653 = -0.2540850123 x = -0.2540850123 Simplifying x = -0.2540850123Subproblem 2
x + 0.4081632653 = -0.154078253 Simplifying x + 0.4081632653 = -0.154078253 Reorder the terms: 0.4081632653 + x = -0.154078253 Solving 0.4081632653 + x = -0.154078253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + x = -0.154078253 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + x = -0.154078253 + -0.4081632653 x = -0.154078253 + -0.4081632653 Combine like terms: -0.154078253 + -0.4081632653 = -0.5622415183 x = -0.5622415183 Simplifying x = -0.5622415183Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2540850123, -0.5622415183}
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