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Simplifying 1 = 0.8x + x2 Solving 1 = 0.8x + x2 Solving for variable 'x'. Reorder the terms: 1 + -0.8x + -1x2 = 0.8x + -0.8x + x2 + -1x2 Combine like terms: 0.8x + -0.8x = 0.0 1 + -0.8x + -1x2 = 0.0 + x2 + -1x2 1 + -0.8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1 + -0.8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 0.8x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.8x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.8x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.8x + x2 = 0 + 1 0.8x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.8x + x2 = 1 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 1 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 1 + 0.16 Combine like terms: 1 + 0.16 = 1.16 0.16 + 0.8x + x2 = 1.16 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (x + 0.4) equal to 1.077032961 and -1.077032961.Subproblem 1
x + 0.4 = 1.077032961 Simplifying x + 0.4 = 1.077032961 Reorder the terms: 0.4 + x = 1.077032961 Solving 0.4 + x = 1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.077032961 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.077032961 + -0.4 x = 1.077032961 + -0.4 Combine like terms: 1.077032961 + -0.4 = 0.677032961 x = 0.677032961 Simplifying x = 0.677032961Subproblem 2
x + 0.4 = -1.077032961 Simplifying x + 0.4 = -1.077032961 Reorder the terms: 0.4 + x = -1.077032961 Solving 0.4 + x = -1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.077032961 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.077032961 + -0.4 x = -1.077032961 + -0.4 Combine like terms: -1.077032961 + -0.4 = -1.477032961 x = -1.477032961 Simplifying x = -1.477032961Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.677032961, -1.477032961}
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