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Simplifying -4.9x2 + 10x + 8 = 0 Reorder the terms: 8 + 10x + -4.9x2 = 0 Solving 8 + 10x + -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'. -1.632653061 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '1.632653061' to each side of the equation. -1.632653061 + -2.040816327x + 1.632653061 + x2 = 0 + 1.632653061 Reorder the terms: -1.632653061 + 1.632653061 + -2.040816327x + x2 = 0 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + -2.040816327x + x2 = 0 + 1.632653061 -2.040816327x + x2 = 0 + 1.632653061 Combine like terms: 0 + 1.632653061 = 1.632653061 -2.040816327x + x2 = 1.632653061 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 = 1.632653061 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 1.632653061 + 1.041232821 Combine like terms: 1.632653061 + 1.041232821 = 2.673885882 1.041232821 + -2.040816327x + x2 = 2.673885882 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 2.673885882 Calculate the square root of the right side: 1.635202092 Break this problem into two subproblems by setting (x + -1.020408164) equal to 1.635202092 and -1.635202092.Subproblem 1
x + -1.020408164 = 1.635202092 Simplifying x + -1.020408164 = 1.635202092 Reorder the terms: -1.020408164 + x = 1.635202092 Solving -1.020408164 + x = 1.635202092 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 = 1.635202092 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 1.635202092 + 1.020408164 x = 1.635202092 + 1.020408164 Combine like terms: 1.635202092 + 1.020408164 = 2.655610256 x = 2.655610256 Simplifying x = 2.655610256Subproblem 2
x + -1.020408164 = -1.635202092 Simplifying x + -1.020408164 = -1.635202092 Reorder the terms: -1.020408164 + x = -1.635202092 Solving -1.020408164 + x = -1.635202092 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 = -1.635202092 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -1.635202092 + 1.020408164 x = -1.635202092 + 1.020408164 Combine like terms: -1.635202092 + 1.020408164 = -0.614793928 x = -0.614793928 Simplifying x = -0.614793928Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.655610256, -0.614793928}
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