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Simplifying x2 + -4x + 6 = 0.49x + 1 Reorder the terms: 6 + -4x + x2 = 0.49x + 1 Reorder the terms: 6 + -4x + x2 = 1 + 0.49x Solving 6 + -4x + x2 = 1 + 0.49x Solving for variable 'x'. Reorder the terms: 6 + -1 + -4x + -0.49x + x2 = 1 + 0.49x + -1 + -0.49x Combine like terms: 6 + -1 = 5 5 + -4x + -0.49x + x2 = 1 + 0.49x + -1 + -0.49x Combine like terms: -4x + -0.49x = -4.49x 5 + -4.49x + x2 = 1 + 0.49x + -1 + -0.49x Reorder the terms: 5 + -4.49x + x2 = 1 + -1 + 0.49x + -0.49x Combine like terms: 1 + -1 = 0 5 + -4.49x + x2 = 0 + 0.49x + -0.49x 5 + -4.49x + x2 = 0.49x + -0.49x Combine like terms: 0.49x + -0.49x = 0.00 5 + -4.49x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4.49x + -5 + x2 = 0.00 + -5 Reorder the terms: 5 + -5 + -4.49x + x2 = 0.00 + -5 Combine like terms: 5 + -5 = 0 0 + -4.49x + x2 = 0.00 + -5 -4.49x + x2 = 0.00 + -5 Combine like terms: 0.00 + -5 = -5 -4.49x + x2 = -5 The x term is -4.49x. Take half its coefficient (-2.245). Square it (5.040025) and add it to both sides. Add '5.040025' to each side of the equation. -4.49x + 5.040025 + x2 = -5 + 5.040025 Reorder the terms: 5.040025 + -4.49x + x2 = -5 + 5.040025 Combine like terms: -5 + 5.040025 = 0.040025 5.040025 + -4.49x + x2 = 0.040025 Factor a perfect square on the left side: (x + -2.245)(x + -2.245) = 0.040025 Calculate the square root of the right side: 0.20006249 Break this problem into two subproblems by setting (x + -2.245) equal to 0.20006249 and -0.20006249.Subproblem 1
x + -2.245 = 0.20006249 Simplifying x + -2.245 = 0.20006249 Reorder the terms: -2.245 + x = 0.20006249 Solving -2.245 + x = 0.20006249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.245' to each side of the equation. -2.245 + 2.245 + x = 0.20006249 + 2.245 Combine like terms: -2.245 + 2.245 = 0.000 0.000 + x = 0.20006249 + 2.245 x = 0.20006249 + 2.245 Combine like terms: 0.20006249 + 2.245 = 2.44506249 x = 2.44506249 Simplifying x = 2.44506249Subproblem 2
x + -2.245 = -0.20006249 Simplifying x + -2.245 = -0.20006249 Reorder the terms: -2.245 + x = -0.20006249 Solving -2.245 + x = -0.20006249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.245' to each side of the equation. -2.245 + 2.245 + x = -0.20006249 + 2.245 Combine like terms: -2.245 + 2.245 = 0.000 0.000 + x = -0.20006249 + 2.245 x = -0.20006249 + 2.245 Combine like terms: -0.20006249 + 2.245 = 2.04493751 x = 2.04493751 Simplifying x = 2.04493751Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.44506249, 2.04493751}
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