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Simplifying 0 = -0.2x2 + 4x + -4.4 Reorder the terms: 0 = -4.4 + 4x + -0.2x2 Solving 0 = -4.4 + 4x + -0.2x2 Solving for variable 'x'. Combine like terms: 0 + 4.4 = 4.4 4.4 + -4x + 0.2x2 = -4.4 + 4x + -0.2x2 + 4.4 + -4x + 0.2x2 Reorder the terms: 4.4 + -4x + 0.2x2 = -4.4 + 4.4 + 4x + -4x + -0.2x2 + 0.2x2 Combine like terms: -4.4 + 4.4 = 0.0 4.4 + -4x + 0.2x2 = 0.0 + 4x + -4x + -0.2x2 + 0.2x2 4.4 + -4x + 0.2x2 = 4x + -4x + -0.2x2 + 0.2x2 Combine like terms: 4x + -4x = 0 4.4 + -4x + 0.2x2 = 0 + -0.2x2 + 0.2x2 4.4 + -4x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 4.4 + -4x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 22 + -20x + x2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -20x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -20x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -20x + x2 = 0 + -22 -20x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -20x + x2 = -22 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -22 + 100 Reorder the terms: 100 + -20x + x2 = -22 + 100 Combine like terms: -22 + 100 = 78 100 + -20x + x2 = 78 Factor a perfect square on the left side: (x + -10)(x + -10) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + -10) equal to 8.831760866 and -8.831760866.Subproblem 1
x + -10 = 8.831760866 Simplifying x + -10 = 8.831760866 Reorder the terms: -10 + x = 8.831760866 Solving -10 + x = 8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.831760866 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.831760866 + 10 x = 8.831760866 + 10 Combine like terms: 8.831760866 + 10 = 18.831760866 x = 18.831760866 Simplifying x = 18.831760866Subproblem 2
x + -10 = -8.831760866 Simplifying x + -10 = -8.831760866 Reorder the terms: -10 + x = -8.831760866 Solving -10 + x = -8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.831760866 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.831760866 + 10 x = -8.831760866 + 10 Combine like terms: -8.831760866 + 10 = 1.168239134 x = 1.168239134 Simplifying x = 1.168239134Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.831760866, 1.168239134}
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