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Simplifying x + -1x2 = 0.18 Solving x + -1x2 = 0.18 Solving for variable 'x'. Reorder the terms: -0.18 + x + -1x2 = 0.18 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 -0.18 + x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.18 + -1x + x2 = 0.00 Move the constant term to the right: Add '-0.18' to each side of the equation. 0.18 + -1x + -0.18 + x2 = 0.00 + -0.18 Reorder the terms: 0.18 + -0.18 + -1x + x2 = 0.00 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + -1x + x2 = 0.00 + -0.18 -1x + x2 = 0.00 + -0.18 Combine like terms: 0.00 + -0.18 = -0.18 -1x + x2 = -0.18 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 = -0.18 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.18 + 0.25 Combine like terms: -0.18 + 0.25 = 0.07 0.25 + -1x + x2 = 0.07 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.07 Calculate the square root of the right side: 0.264575131 Break this problem into two subproblems by setting (x + 0.5) equal to 0.264575131 and -0.264575131.Subproblem 1
x + 0.5 = 0.264575131 Simplifying x + 0.5 = 0.264575131 Reorder the terms: 0.5 + x = 0.264575131 Solving 0.5 + x = 0.264575131 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 = 0.264575131 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.264575131 + -0.5 x = 0.264575131 + -0.5 Combine like terms: 0.264575131 + -0.5 = -0.235424869 x = -0.235424869 Simplifying x = -0.235424869Subproblem 2
x + 0.5 = -0.264575131 Simplifying x + 0.5 = -0.264575131 Reorder the terms: 0.5 + x = -0.264575131 Solving 0.5 + x = -0.264575131 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 = -0.264575131 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.264575131 + -0.5 x = -0.264575131 + -0.5 Combine like terms: -0.264575131 + -0.5 = -0.764575131 x = -0.764575131 Simplifying x = -0.764575131Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.235424869, -0.764575131}
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