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Simplifying 0 = 4.9x2 + 10x + -10 Reorder the terms: 0 = -10 + 10x + 4.9x2 Solving 0 = -10 + 10x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -10x + -4.9x2 = -10 + 10x + 4.9x2 + 10 + -10x + -4.9x2 Reorder the terms: 10 + -10x + -4.9x2 = -10 + 10 + 10x + -10x + 4.9x2 + -4.9x2 Combine like terms: -10 + 10 = 0 10 + -10x + -4.9x2 = 0 + 10x + -10x + 4.9x2 + -4.9x2 10 + -10x + -4.9x2 = 10x + -10x + 4.9x2 + -4.9x2 Combine like terms: 10x + -10x = 0 10 + -10x + -4.9x2 = 0 + 4.9x2 + -4.9x2 10 + -10x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 10 + -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'. -2.040816327 + 2.040816327x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 2.040816327x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 2.040816327x + x2 = 0 + 2.040816327 2.040816327x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 2.040816327x + x2 = 2.040816327 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 = 2.040816327 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327x + x2 = 2.040816327 + 1.041232821 Combine like terms: 2.040816327 + 1.041232821 = 3.082049148 1.041232821 + 2.040816327x + x2 = 3.082049148 Factor a perfect square on the left side: (x + 1.020408164)(x + 1.020408164) = 3.082049148 Calculate the square root of the right side: 1.755576586 Break this problem into two subproblems by setting (x + 1.020408164) equal to 1.755576586 and -1.755576586.Subproblem 1
x + 1.020408164 = 1.755576586 Simplifying x + 1.020408164 = 1.755576586 Reorder the terms: 1.020408164 + x = 1.755576586 Solving 1.020408164 + x = 1.755576586 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 = 1.755576586 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = 1.755576586 + -1.020408164 x = 1.755576586 + -1.020408164 Combine like terms: 1.755576586 + -1.020408164 = 0.735168422 x = 0.735168422 Simplifying x = 0.735168422Subproblem 2
x + 1.020408164 = -1.755576586 Simplifying x + 1.020408164 = -1.755576586 Reorder the terms: 1.020408164 + x = -1.755576586 Solving 1.020408164 + x = -1.755576586 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 = -1.755576586 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = -1.755576586 + -1.020408164 x = -1.755576586 + -1.020408164 Combine like terms: -1.755576586 + -1.020408164 = -2.77598475 x = -2.77598475 Simplifying x = -2.77598475Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.735168422, -2.77598475}
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