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Simplifying 4.9x2 + 900x + 24 = 0 Reorder the terms: 24 + 900x + 4.9x2 = 0 Solving 24 + 900x + 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'. 4.897959184 + 183.6734694x + x2 = 0 Move the constant term to the right: Add '-4.897959184' to each side of the equation. 4.897959184 + 183.6734694x + -4.897959184 + x2 = 0 + -4.897959184 Reorder the terms: 4.897959184 + -4.897959184 + 183.6734694x + x2 = 0 + -4.897959184 Combine like terms: 4.897959184 + -4.897959184 = 0.000000000 0.000000000 + 183.6734694x + x2 = 0 + -4.897959184 183.6734694x + x2 = 0 + -4.897959184 Combine like terms: 0 + -4.897959184 = -4.897959184 183.6734694x + x2 = -4.897959184 The x term is 183.6734694x. Take half its coefficient (91.8367347). Square it (8433.985840) and add it to both sides. Add '8433.985840' to each side of the equation. 183.6734694x + 8433.985840 + x2 = -4.897959184 + 8433.985840 Reorder the terms: 8433.985840 + 183.6734694x + x2 = -4.897959184 + 8433.985840 Combine like terms: -4.897959184 + 8433.985840 = 8429.087880816 8433.985840 + 183.6734694x + x2 = 8429.087880816 Factor a perfect square on the left side: (x + 91.8367347)(x + 91.8367347) = 8429.087880816 Calculate the square root of the right side: 91.810064159 Break this problem into two subproblems by setting (x + 91.8367347) equal to 91.810064159 and -91.810064159.Subproblem 1
x + 91.8367347 = 91.810064159 Simplifying x + 91.8367347 = 91.810064159 Reorder the terms: 91.8367347 + x = 91.810064159 Solving 91.8367347 + x = 91.810064159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-91.8367347' to each side of the equation. 91.8367347 + -91.8367347 + x = 91.810064159 + -91.8367347 Combine like terms: 91.8367347 + -91.8367347 = 0.0000000 0.0000000 + x = 91.810064159 + -91.8367347 x = 91.810064159 + -91.8367347 Combine like terms: 91.810064159 + -91.8367347 = -0.026670541 x = -0.026670541 Simplifying x = -0.026670541Subproblem 2
x + 91.8367347 = -91.810064159 Simplifying x + 91.8367347 = -91.810064159 Reorder the terms: 91.8367347 + x = -91.810064159 Solving 91.8367347 + x = -91.810064159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-91.8367347' to each side of the equation. 91.8367347 + -91.8367347 + x = -91.810064159 + -91.8367347 Combine like terms: 91.8367347 + -91.8367347 = 0.0000000 0.0000000 + x = -91.810064159 + -91.8367347 x = -91.810064159 + -91.8367347 Combine like terms: -91.810064159 + -91.8367347 = -183.646798859 x = -183.646798859 Simplifying x = -183.646798859Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.026670541, -183.646798859}
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