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Simplifying 1.25x2 = x + 1 Reorder the terms: 1.25x2 = 1 + x Solving 1.25x2 = 1 + x Solving for variable 'x'. Reorder the terms: -1 + -1x + 1.25x2 = 1 + x + -1 + -1x Reorder the terms: -1 + -1x + 1.25x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -1 + -1x + 1.25x2 = 0 + x + -1x -1 + -1x + 1.25x2 = x + -1x Combine like terms: x + -1x = 0 -1 + -1x + 1.25x2 = 0 Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -0.8 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.8x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.8x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.8x + x2 = 0 + 0.8 -0.8x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.8x + x2 = 0.8 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 = 0.8 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.8 + 0.16 Combine like terms: 0.8 + 0.16 = 0.96 0.16 + -0.8x + x2 = 0.96 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + -0.4) equal to 0.979795897 and -0.979795897.Subproblem 1
x + -0.4 = 0.979795897 Simplifying x + -0.4 = 0.979795897 Reorder the terms: -0.4 + x = 0.979795897 Solving -0.4 + x = 0.979795897 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 = 0.979795897 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.979795897 + 0.4 x = 0.979795897 + 0.4 Combine like terms: 0.979795897 + 0.4 = 1.379795897 x = 1.379795897 Simplifying x = 1.379795897Subproblem 2
x + -0.4 = -0.979795897 Simplifying x + -0.4 = -0.979795897 Reorder the terms: -0.4 + x = -0.979795897 Solving -0.4 + x = -0.979795897 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 = -0.979795897 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.979795897 + 0.4 x = -0.979795897 + 0.4 Combine like terms: -0.979795897 + 0.4 = -0.579795897 x = -0.579795897 Simplifying x = -0.579795897Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.379795897, -0.579795897}
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