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Simplifying -1x2 + -0.18x + 0.045 = 0 Reorder the terms: 0.045 + -0.18x + -1x2 = 0 Solving 0.045 + -0.18x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.045 + 0.18x + x2 = 0 Move the constant term to the right: Add '0.045' to each side of the equation. -0.045 + 0.18x + 0.045 + x2 = 0 + 0.045 Reorder the terms: -0.045 + 0.045 + 0.18x + x2 = 0 + 0.045 Combine like terms: -0.045 + 0.045 = 0.000 0.000 + 0.18x + x2 = 0 + 0.045 0.18x + x2 = 0 + 0.045 Combine like terms: 0 + 0.045 = 0.045 0.18x + x2 = 0.045 The x term is 0.18x. Take half its coefficient (0.09). Square it (0.0081) and add it to both sides. Add '0.0081' to each side of the equation. 0.18x + 0.0081 + x2 = 0.045 + 0.0081 Reorder the terms: 0.0081 + 0.18x + x2 = 0.045 + 0.0081 Combine like terms: 0.045 + 0.0081 = 0.0531 0.0081 + 0.18x + x2 = 0.0531 Factor a perfect square on the left side: (x + 0.09)(x + 0.09) = 0.0531 Calculate the square root of the right side: 0.230434372 Break this problem into two subproblems by setting (x + 0.09) equal to 0.230434372 and -0.230434372.Subproblem 1
x + 0.09 = 0.230434372 Simplifying x + 0.09 = 0.230434372 Reorder the terms: 0.09 + x = 0.230434372 Solving 0.09 + x = 0.230434372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09' to each side of the equation. 0.09 + -0.09 + x = 0.230434372 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + x = 0.230434372 + -0.09 x = 0.230434372 + -0.09 Combine like terms: 0.230434372 + -0.09 = 0.140434372 x = 0.140434372 Simplifying x = 0.140434372Subproblem 2
x + 0.09 = -0.230434372 Simplifying x + 0.09 = -0.230434372 Reorder the terms: 0.09 + x = -0.230434372 Solving 0.09 + x = -0.230434372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09' to each side of the equation. 0.09 + -0.09 + x = -0.230434372 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + x = -0.230434372 + -0.09 x = -0.230434372 + -0.09 Combine like terms: -0.230434372 + -0.09 = -0.320434372 x = -0.320434372 Simplifying x = -0.320434372Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.140434372, -0.320434372}
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