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Simplifying x2 + -1x = 0.95 Reorder the terms: -1x + x2 = 0.95 Solving -1x + x2 = 0.95 Solving for variable 'x'. Reorder the terms: -0.95 + -1x + x2 = 0.95 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 -0.95 + -1x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.95' to each side of the equation. -0.95 + -1x + 0.95 + x2 = 0.00 + 0.95 Reorder the terms: -0.95 + 0.95 + -1x + x2 = 0.00 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + -1x + x2 = 0.00 + 0.95 -1x + x2 = 0.00 + 0.95 Combine like terms: 0.00 + 0.95 = 0.95 -1x + x2 = 0.95 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.95 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.95 + 0.25 Combine like terms: 0.95 + 0.25 = 1.2 0.25 + -1x + x2 = 1.2 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (x + -0.5) equal to 1.095445115 and -1.095445115.Subproblem 1
x + -0.5 = 1.095445115 Simplifying x + -0.5 = 1.095445115 Reorder the terms: -0.5 + x = 1.095445115 Solving -0.5 + x = 1.095445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.095445115 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.095445115 + 0.5 x = 1.095445115 + 0.5 Combine like terms: 1.095445115 + 0.5 = 1.595445115 x = 1.595445115 Simplifying x = 1.595445115Subproblem 2
x + -0.5 = -1.095445115 Simplifying x + -0.5 = -1.095445115 Reorder the terms: -0.5 + x = -1.095445115 Solving -0.5 + x = -1.095445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.095445115 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.095445115 + 0.5 x = -1.095445115 + 0.5 Combine like terms: -1.095445115 + 0.5 = -0.595445115 x = -0.595445115 Simplifying x = -0.595445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.595445115, -0.595445115}
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