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Simplifying -4.9x2 + 9.8x = 3 Reorder the terms: 9.8x + -4.9x2 = 3 Solving 9.8x + -4.9x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 9.8x + -4.9x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 9.8x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.612244898 + -2x + x2 = 0 Move the constant term to the right: Add '-0.612244898' to each side of the equation. 0.612244898 + -2x + -0.612244898 + x2 = 0 + -0.612244898 Reorder the terms: 0.612244898 + -0.612244898 + -2x + x2 = 0 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + -2x + x2 = 0 + -0.612244898 -2x + x2 = 0 + -0.612244898 Combine like terms: 0 + -0.612244898 = -0.612244898 -2x + x2 = -0.612244898 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.612244898 + 1 Reorder the terms: 1 + -2x + x2 = -0.612244898 + 1 Combine like terms: -0.612244898 + 1 = 0.387755102 1 + -2x + x2 = 0.387755102 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.387755102 Calculate the square root of the right side: 0.622699849 Break this problem into two subproblems by setting (x + -1) equal to 0.622699849 and -0.622699849.Subproblem 1
x + -1 = 0.622699849 Simplifying x + -1 = 0.622699849 Reorder the terms: -1 + x = 0.622699849 Solving -1 + x = 0.622699849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.622699849 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.622699849 + 1 x = 0.622699849 + 1 Combine like terms: 0.622699849 + 1 = 1.622699849 x = 1.622699849 Simplifying x = 1.622699849Subproblem 2
x + -1 = -0.622699849 Simplifying x + -1 = -0.622699849 Reorder the terms: -1 + x = -0.622699849 Solving -1 + x = -0.622699849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.622699849 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.622699849 + 1 x = -0.622699849 + 1 Combine like terms: -0.622699849 + 1 = 0.377300151 x = 0.377300151 Simplifying x = 0.377300151Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.622699849, 0.377300151}
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