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Simplifying x + -1x2 = 0.147456 Solving x + -1x2 = 0.147456 Solving for variable 'x'. Reorder the terms: -0.147456 + x + -1x2 = 0.147456 + -0.147456 Combine like terms: 0.147456 + -0.147456 = 0.000000 -0.147456 + x + -1x2 = 0.000000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.147456 + -1x + x2 = 0.000000 Move the constant term to the right: Add '-0.147456' to each side of the equation. 0.147456 + -1x + -0.147456 + x2 = 0.000000 + -0.147456 Reorder the terms: 0.147456 + -0.147456 + -1x + x2 = 0.000000 + -0.147456 Combine like terms: 0.147456 + -0.147456 = 0.000000 0.000000 + -1x + x2 = 0.000000 + -0.147456 -1x + x2 = 0.000000 + -0.147456 Combine like terms: 0.000000 + -0.147456 = -0.147456 -1x + x2 = -0.147456 The x term is x. 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 = -0.147456 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.147456 + 0.25 Combine like terms: -0.147456 + 0.25 = 0.102544 0.25 + -1x + x2 = 0.102544 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.102544 Calculate the square root of the right side: 0.320224921 Break this problem into two subproblems by setting (x + 0.5) equal to 0.320224921 and -0.320224921.Subproblem 1
x + 0.5 = 0.320224921 Simplifying x + 0.5 = 0.320224921 Reorder the terms: 0.5 + x = 0.320224921 Solving 0.5 + x = 0.320224921 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 = 0.320224921 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.320224921 + -0.5 x = 0.320224921 + -0.5 Combine like terms: 0.320224921 + -0.5 = -0.179775079 x = -0.179775079 Simplifying x = -0.179775079Subproblem 2
x + 0.5 = -0.320224921 Simplifying x + 0.5 = -0.320224921 Reorder the terms: 0.5 + x = -0.320224921 Solving 0.5 + x = -0.320224921 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 = -0.320224921 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.320224921 + -0.5 x = -0.320224921 + -0.5 Combine like terms: -0.320224921 + -0.5 = -0.820224921 x = -0.820224921 Simplifying x = -0.820224921Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.179775079, -0.820224921}
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