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Simplifying x2 + 0.43x + -2.8294 = 0 Reorder the terms: -2.8294 + 0.43x + x2 = 0 Solving -2.8294 + 0.43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.8294' to each side of the equation. -2.8294 + 0.43x + 2.8294 + x2 = 0 + 2.8294 Reorder the terms: -2.8294 + 2.8294 + 0.43x + x2 = 0 + 2.8294 Combine like terms: -2.8294 + 2.8294 = 0.0000 0.0000 + 0.43x + x2 = 0 + 2.8294 0.43x + x2 = 0 + 2.8294 Combine like terms: 0 + 2.8294 = 2.8294 0.43x + x2 = 2.8294 The x term is 0.43x. Take half its coefficient (0.215). Square it (0.046225) and add it to both sides. Add '0.046225' to each side of the equation. 0.43x + 0.046225 + x2 = 2.8294 + 0.046225 Reorder the terms: 0.046225 + 0.43x + x2 = 2.8294 + 0.046225 Combine like terms: 2.8294 + 0.046225 = 2.875625 0.046225 + 0.43x + x2 = 2.875625 Factor a perfect square on the left side: (x + 0.215)(x + 0.215) = 2.875625 Calculate the square root of the right side: 1.695766788 Break this problem into two subproblems by setting (x + 0.215) equal to 1.695766788 and -1.695766788.Subproblem 1
x + 0.215 = 1.695766788 Simplifying x + 0.215 = 1.695766788 Reorder the terms: 0.215 + x = 1.695766788 Solving 0.215 + x = 1.695766788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.215' to each side of the equation. 0.215 + -0.215 + x = 1.695766788 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = 1.695766788 + -0.215 x = 1.695766788 + -0.215 Combine like terms: 1.695766788 + -0.215 = 1.480766788 x = 1.480766788 Simplifying x = 1.480766788Subproblem 2
x + 0.215 = -1.695766788 Simplifying x + 0.215 = -1.695766788 Reorder the terms: 0.215 + x = -1.695766788 Solving 0.215 + x = -1.695766788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.215' to each side of the equation. 0.215 + -0.215 + x = -1.695766788 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = -1.695766788 + -0.215 x = -1.695766788 + -0.215 Combine like terms: -1.695766788 + -0.215 = -1.910766788 x = -1.910766788 Simplifying x = -1.910766788Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.480766788, -1.910766788}
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