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Simplifying 0.5 + -0.1x = 45x + -187x2 Solving 0.5 + -0.1x = 45x + -187x2 Solving for variable 'x'. Combine like terms: -0.1x + -45x = -45.1x 0.5 + -45.1x + 187x2 = 45x + -187x2 + -45x + 187x2 Reorder the terms: 0.5 + -45.1x + 187x2 = 45x + -45x + -187x2 + 187x2 Combine like terms: 45x + -45x = 0 0.5 + -45.1x + 187x2 = 0 + -187x2 + 187x2 0.5 + -45.1x + 187x2 = -187x2 + 187x2 Combine like terms: -187x2 + 187x2 = 0 0.5 + -45.1x + 187x2 = 0 Begin completing the square. Divide all terms by 187 the coefficient of the squared term: Divide each side by '187'. 0.002673796791 + -0.2411764706x + x2 = 0 Move the constant term to the right: Add '-0.002673796791' to each side of the equation. 0.002673796791 + -0.2411764706x + -0.002673796791 + x2 = 0 + -0.002673796791 Reorder the terms: 0.002673796791 + -0.002673796791 + -0.2411764706x + x2 = 0 + -0.002673796791 Combine like terms: 0.002673796791 + -0.002673796791 = 0.000000000000 0.000000000000 + -0.2411764706x + x2 = 0 + -0.002673796791 -0.2411764706x + x2 = 0 + -0.002673796791 Combine like terms: 0 + -0.002673796791 = -0.002673796791 -0.2411764706x + x2 = -0.002673796791 The x term is -0.2411764706x. Take half its coefficient (-0.1205882353). Square it (0.01454152249) and add it to both sides. Add '0.01454152249' to each side of the equation. -0.2411764706x + 0.01454152249 + x2 = -0.002673796791 + 0.01454152249 Reorder the terms: 0.01454152249 + -0.2411764706x + x2 = -0.002673796791 + 0.01454152249 Combine like terms: -0.002673796791 + 0.01454152249 = 0.011867725699 0.01454152249 + -0.2411764706x + x2 = 0.011867725699 Factor a perfect square on the left side: (x + -0.1205882353)(x + -0.1205882353) = 0.011867725699 Calculate the square root of the right side: 0.108939092 Break this problem into two subproblems by setting (x + -0.1205882353) equal to 0.108939092 and -0.108939092.Subproblem 1
x + -0.1205882353 = 0.108939092 Simplifying x + -0.1205882353 = 0.108939092 Reorder the terms: -0.1205882353 + x = 0.108939092 Solving -0.1205882353 + x = 0.108939092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1205882353' to each side of the equation. -0.1205882353 + 0.1205882353 + x = 0.108939092 + 0.1205882353 Combine like terms: -0.1205882353 + 0.1205882353 = 0.0000000000 0.0000000000 + x = 0.108939092 + 0.1205882353 x = 0.108939092 + 0.1205882353 Combine like terms: 0.108939092 + 0.1205882353 = 0.2295273273 x = 0.2295273273 Simplifying x = 0.2295273273Subproblem 2
x + -0.1205882353 = -0.108939092 Simplifying x + -0.1205882353 = -0.108939092 Reorder the terms: -0.1205882353 + x = -0.108939092 Solving -0.1205882353 + x = -0.108939092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1205882353' to each side of the equation. -0.1205882353 + 0.1205882353 + x = -0.108939092 + 0.1205882353 Combine like terms: -0.1205882353 + 0.1205882353 = 0.0000000000 0.0000000000 + x = -0.108939092 + 0.1205882353 x = -0.108939092 + 0.1205882353 Combine like terms: -0.108939092 + 0.1205882353 = 0.0116491433 x = 0.0116491433 Simplifying x = 0.0116491433Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2295273273, 0.0116491433}
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