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Simplifying -4.9x2 + 19.6x + 2 = 0 Reorder the terms: 2 + 19.6x + -4.9x2 = 0 Solving 2 + 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'. -0.4081632653 + -4x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -4x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -4x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + 0.4081632653 -4x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -4x + x2 = 0.4081632653 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 = 0.4081632653 + 4 Reorder the terms: 4 + -4x + x2 = 0.4081632653 + 4 Combine like terms: 0.4081632653 + 4 = 4.4081632653 4 + -4x + x2 = 4.4081632653 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.4081632653 Calculate the square root of the right side: 2.099562637 Break this problem into two subproblems by setting (x + -2) equal to 2.099562637 and -2.099562637.Subproblem 1
x + -2 = 2.099562637 Simplifying x + -2 = 2.099562637 Reorder the terms: -2 + x = 2.099562637 Solving -2 + x = 2.099562637 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 = 2.099562637 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.099562637 + 2 x = 2.099562637 + 2 Combine like terms: 2.099562637 + 2 = 4.099562637 x = 4.099562637 Simplifying x = 4.099562637Subproblem 2
x + -2 = -2.099562637 Simplifying x + -2 = -2.099562637 Reorder the terms: -2 + x = -2.099562637 Solving -2 + x = -2.099562637 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 = -2.099562637 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.099562637 + 2 x = -2.099562637 + 2 Combine like terms: -2.099562637 + 2 = -0.099562637 x = -0.099562637 Simplifying x = -0.099562637Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.099562637, -0.099562637}
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