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Simplifying (x2 + -1x + 0.25) = (0.3 + x) Reorder the terms: (0.25 + -1x + x2) = (0.3 + x) Remove parenthesis around (0.25 + -1x + x2) 0.25 + -1x + x2 = (0.3 + x) Remove parenthesis around (0.3 + x) 0.25 + -1x + x2 = 0.3 + x Solving 0.25 + -1x + x2 = 0.3 + x Solving for variable 'x'. Reorder the terms: 0.25 + -0.3 + -1x + -1x + x2 = 0.3 + x + -0.3 + -1x Combine like terms: 0.25 + -0.3 = -0.05 -0.05 + -1x + -1x + x2 = 0.3 + x + -0.3 + -1x Combine like terms: -1x + -1x = -2x -0.05 + -2x + x2 = 0.3 + x + -0.3 + -1x Reorder the terms: -0.05 + -2x + x2 = 0.3 + -0.3 + x + -1x Combine like terms: 0.3 + -0.3 = 0.0 -0.05 + -2x + x2 = 0.0 + x + -1x -0.05 + -2x + x2 = x + -1x Combine like terms: x + -1x = 0 -0.05 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + -2x + 0.05 + x2 = 0 + 0.05 Reorder the terms: -0.05 + 0.05 + -2x + x2 = 0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + -2x + x2 = 0 + 0.05 -2x + x2 = 0 + 0.05 Combine like terms: 0 + 0.05 = 0.05 -2x + x2 = 0.05 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 = 0.05 + 1 Reorder the terms: 1 + -2x + x2 = 0.05 + 1 Combine like terms: 0.05 + 1 = 1.05 1 + -2x + x2 = 1.05 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.05 Calculate the square root of the right side: 1.024695077 Break this problem into two subproblems by setting (x + -1) equal to 1.024695077 and -1.024695077.Subproblem 1
x + -1 = 1.024695077 Simplifying x + -1 = 1.024695077 Reorder the terms: -1 + x = 1.024695077 Solving -1 + x = 1.024695077 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 = 1.024695077 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.024695077 + 1 x = 1.024695077 + 1 Combine like terms: 1.024695077 + 1 = 2.024695077 x = 2.024695077 Simplifying x = 2.024695077Subproblem 2
x + -1 = -1.024695077 Simplifying x + -1 = -1.024695077 Reorder the terms: -1 + x = -1.024695077 Solving -1 + x = -1.024695077 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 = -1.024695077 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.024695077 + 1 x = -1.024695077 + 1 Combine like terms: -1.024695077 + 1 = -0.024695077 x = -0.024695077 Simplifying x = -0.024695077Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.024695077, -0.024695077}
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