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Simplifying 4.9x2 + -19.6x + 3.96 = 0 Reorder the terms: 3.96 + -19.6x + 4.9x2 = 0 Solving 3.96 + -19.6x + 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'. 0.8081632653 + -4x + x2 = 0 Move the constant term to the right: Add '-0.8081632653' to each side of the equation. 0.8081632653 + -4x + -0.8081632653 + x2 = 0 + -0.8081632653 Reorder the terms: 0.8081632653 + -0.8081632653 + -4x + x2 = 0 + -0.8081632653 Combine like terms: 0.8081632653 + -0.8081632653 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.8081632653 -4x + x2 = 0 + -0.8081632653 Combine like terms: 0 + -0.8081632653 = -0.8081632653 -4x + x2 = -0.8081632653 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.8081632653 + 4 Reorder the terms: 4 + -4x + x2 = -0.8081632653 + 4 Combine like terms: -0.8081632653 + 4 = 3.1918367347 4 + -4x + x2 = 3.1918367347 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.1918367347 Calculate the square root of the right side: 1.786571223 Break this problem into two subproblems by setting (x + -2) equal to 1.786571223 and -1.786571223.Subproblem 1
x + -2 = 1.786571223 Simplifying x + -2 = 1.786571223 Reorder the terms: -2 + x = 1.786571223 Solving -2 + x = 1.786571223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.786571223 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.786571223 + 2 x = 1.786571223 + 2 Combine like terms: 1.786571223 + 2 = 3.786571223 x = 3.786571223 Simplifying x = 3.786571223Subproblem 2
x + -2 = -1.786571223 Simplifying x + -2 = -1.786571223 Reorder the terms: -2 + x = -1.786571223 Solving -2 + x = -1.786571223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.786571223 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.786571223 + 2 x = -1.786571223 + 2 Combine like terms: -1.786571223 + 2 = 0.213428777 x = 0.213428777 Simplifying x = 0.213428777Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.786571223, 0.213428777}
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