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Simplifying x2 + 0.43x + -5.2245 = 0 Reorder the terms: -5.2245 + 0.43x + x2 = 0 Solving -5.2245 + 0.43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5.2245' to each side of the equation. -5.2245 + 0.43x + 5.2245 + x2 = 0 + 5.2245 Reorder the terms: -5.2245 + 5.2245 + 0.43x + x2 = 0 + 5.2245 Combine like terms: -5.2245 + 5.2245 = 0.0000 0.0000 + 0.43x + x2 = 0 + 5.2245 0.43x + x2 = 0 + 5.2245 Combine like terms: 0 + 5.2245 = 5.2245 0.43x + x2 = 5.2245 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 = 5.2245 + 0.046225 Reorder the terms: 0.046225 + 0.43x + x2 = 5.2245 + 0.046225 Combine like terms: 5.2245 + 0.046225 = 5.270725 0.046225 + 0.43x + x2 = 5.270725 Factor a perfect square on the left side: (x + 0.215)(x + 0.215) = 5.270725 Calculate the square root of the right side: 2.295805959 Break this problem into two subproblems by setting (x + 0.215) equal to 2.295805959 and -2.295805959.Subproblem 1
x + 0.215 = 2.295805959 Simplifying x + 0.215 = 2.295805959 Reorder the terms: 0.215 + x = 2.295805959 Solving 0.215 + x = 2.295805959 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 = 2.295805959 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = 2.295805959 + -0.215 x = 2.295805959 + -0.215 Combine like terms: 2.295805959 + -0.215 = 2.080805959 x = 2.080805959 Simplifying x = 2.080805959Subproblem 2
x + 0.215 = -2.295805959 Simplifying x + 0.215 = -2.295805959 Reorder the terms: 0.215 + x = -2.295805959 Solving 0.215 + x = -2.295805959 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 = -2.295805959 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = -2.295805959 + -0.215 x = -2.295805959 + -0.215 Combine like terms: -2.295805959 + -0.215 = -2.510805959 x = -2.510805959 Simplifying x = -2.510805959Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.080805959, -2.510805959}
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