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Simplifying 3 = 10x + -4.9x2 Solving 3 = 10x + -4.9x2 Solving for variable 'x'. Reorder the terms: 3 + -10x + 4.9x2 = 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 10x + -10x = 0 3 + -10x + 4.9x2 = 0 + -4.9x2 + 4.9x2 3 + -10x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 3 + -10x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.612244898 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '-0.612244898' to each side of the equation. 0.612244898 + -2.040816327x + -0.612244898 + x2 = 0 + -0.612244898 Reorder the terms: 0.612244898 + -0.612244898 + -2.040816327x + x2 = 0 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + -2.040816327x + x2 = 0 + -0.612244898 -2.040816327x + x2 = 0 + -0.612244898 Combine like terms: 0 + -0.612244898 = -0.612244898 -2.040816327x + x2 = -0.612244898 The x term is -2.040816327x. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327x + 1.041232821 + x2 = -0.612244898 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = -0.612244898 + 1.041232821 Combine like terms: -0.612244898 + 1.041232821 = 0.428987923 1.041232821 + -2.040816327x + x2 = 0.428987923 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 0.428987923 Calculate the square root of the right side: 0.654971696 Break this problem into two subproblems by setting (x + -1.020408164) equal to 0.654971696 and -0.654971696.Subproblem 1
x + -1.020408164 = 0.654971696 Simplifying x + -1.020408164 = 0.654971696 Reorder the terms: -1.020408164 + x = 0.654971696 Solving -1.020408164 + x = 0.654971696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + x = 0.654971696 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 0.654971696 + 1.020408164 x = 0.654971696 + 1.020408164 Combine like terms: 0.654971696 + 1.020408164 = 1.67537986 x = 1.67537986 Simplifying x = 1.67537986Subproblem 2
x + -1.020408164 = -0.654971696 Simplifying x + -1.020408164 = -0.654971696 Reorder the terms: -1.020408164 + x = -0.654971696 Solving -1.020408164 + x = -0.654971696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + x = -0.654971696 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -0.654971696 + 1.020408164 x = -0.654971696 + 1.020408164 Combine like terms: -0.654971696 + 1.020408164 = 0.365436468 x = 0.365436468 Simplifying x = 0.365436468Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.67537986, 0.365436468}
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