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Simplifying 3.9 = -0.5x2 + x + 4 Reorder the terms: 3.9 = 4 + x + -0.5x2 Solving 3.9 = 4 + x + -0.5x2 Solving for variable 'x'. Combine like terms: 3.9 + -4 = -0.1 -0.1 + -1x + 0.5x2 = 4 + x + -0.5x2 + -4 + -1x + 0.5x2 Reorder the terms: -0.1 + -1x + 0.5x2 = 4 + -4 + x + -1x + -0.5x2 + 0.5x2 Combine like terms: 4 + -4 = 0 -0.1 + -1x + 0.5x2 = 0 + x + -1x + -0.5x2 + 0.5x2 -0.1 + -1x + 0.5x2 = x + -1x + -0.5x2 + 0.5x2 Combine like terms: x + -1x = 0 -0.1 + -1x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -0.1 + -1x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -0.1 + -1x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -0.2 + -2x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -2x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -2x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -2x + x2 = 0 + 0.2 -2x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -2x + x2 = 0.2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.2 + 1 Reorder the terms: 1 + -2x + x2 = 0.2 + 1 Combine like terms: 0.2 + 1 = 1.2 1 + -2x + x2 = 1.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (x + -1) equal to 1.095445115 and -1.095445115.Subproblem 1
x + -1 = 1.095445115 Simplifying x + -1 = 1.095445115 Reorder the terms: -1 + x = 1.095445115 Solving -1 + x = 1.095445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.095445115 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.095445115 + 1 x = 1.095445115 + 1 Combine like terms: 1.095445115 + 1 = 2.095445115 x = 2.095445115 Simplifying x = 2.095445115Subproblem 2
x + -1 = -1.095445115 Simplifying x + -1 = -1.095445115 Reorder the terms: -1 + x = -1.095445115 Solving -1 + x = -1.095445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.095445115 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.095445115 + 1 x = -1.095445115 + 1 Combine like terms: -1.095445115 + 1 = -0.095445115 x = -0.095445115 Simplifying x = -0.095445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.095445115, -0.095445115}
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