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Simplifying x2 + 0.43x + -1.4749 = 0 Reorder the terms: -1.4749 + 0.43x + x2 = 0 Solving -1.4749 + 0.43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.4749' to each side of the equation. -1.4749 + 0.43x + 1.4749 + x2 = 0 + 1.4749 Reorder the terms: -1.4749 + 1.4749 + 0.43x + x2 = 0 + 1.4749 Combine like terms: -1.4749 + 1.4749 = 0.0000 0.0000 + 0.43x + x2 = 0 + 1.4749 0.43x + x2 = 0 + 1.4749 Combine like terms: 0 + 1.4749 = 1.4749 0.43x + x2 = 1.4749 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 = 1.4749 + 0.046225 Reorder the terms: 0.046225 + 0.43x + x2 = 1.4749 + 0.046225 Combine like terms: 1.4749 + 0.046225 = 1.521125 0.046225 + 0.43x + x2 = 1.521125 Factor a perfect square on the left side: (x + 0.215)(x + 0.215) = 1.521125 Calculate the square root of the right side: 1.233338964 Break this problem into two subproblems by setting (x + 0.215) equal to 1.233338964 and -1.233338964.Subproblem 1
x + 0.215 = 1.233338964 Simplifying x + 0.215 = 1.233338964 Reorder the terms: 0.215 + x = 1.233338964 Solving 0.215 + x = 1.233338964 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 = 1.233338964 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = 1.233338964 + -0.215 x = 1.233338964 + -0.215 Combine like terms: 1.233338964 + -0.215 = 1.018338964 x = 1.018338964 Simplifying x = 1.018338964Subproblem 2
x + 0.215 = -1.233338964 Simplifying x + 0.215 = -1.233338964 Reorder the terms: 0.215 + x = -1.233338964 Solving 0.215 + x = -1.233338964 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 = -1.233338964 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = -1.233338964 + -0.215 x = -1.233338964 + -0.215 Combine like terms: -1.233338964 + -0.215 = -1.448338964 x = -1.448338964 Simplifying x = -1.448338964Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.018338964, -1.448338964}
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