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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 = 1.653477719 1.041232821 + 2.040816327x + x2 = 1.653477719 Factor a perfect square on the left side: (x + 1.020408164)(x + 1.020408164) = 1.653477719 Calculate the square root of the right side: 1.285876246 Break this problem into two subproblems by setting (x + 1.020408164) equal to 1.285876246 and -1.285876246.Subproblem 1
x + 1.020408164 = 1.285876246 Simplifying x + 1.020408164 = 1.285876246 Reorder the terms: 1.020408164 + x = 1.285876246 Solving 1.020408164 + x = 1.285876246 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 = 1.285876246 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = 1.285876246 + -1.020408164 x = 1.285876246 + -1.020408164 Combine like terms: 1.285876246 + -1.020408164 = 0.265468082 x = 0.265468082 Simplifying x = 0.265468082Subproblem 2
x + 1.020408164 = -1.285876246 Simplifying x + 1.020408164 = -1.285876246 Reorder the terms: 1.020408164 + x = -1.285876246 Solving 1.020408164 + x = -1.285876246 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 = -1.285876246 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = -1.285876246 + -1.020408164 x = -1.285876246 + -1.020408164 Combine like terms: -1.285876246 + -1.020408164 = -2.30628441 x = -2.30628441 Simplifying x = -2.30628441Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.265468082, -2.30628441}
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