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Simplifying 0.15x2 + 0.1037x + -0.0174 = 0 Reorder the terms: -0.0174 + 0.1037x + 0.15x2 = 0 Solving -0.0174 + 0.1037x + 0.15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. -0.116 + 0.6913333333x + x2 = 0 Move the constant term to the right: Add '0.116' to each side of the equation. -0.116 + 0.6913333333x + 0.116 + x2 = 0 + 0.116 Reorder the terms: -0.116 + 0.116 + 0.6913333333x + x2 = 0 + 0.116 Combine like terms: -0.116 + 0.116 = 0.000 0.000 + 0.6913333333x + x2 = 0 + 0.116 0.6913333333x + x2 = 0 + 0.116 Combine like terms: 0 + 0.116 = 0.116 0.6913333333x + x2 = 0.116 The x term is 0.6913333333x. Take half its coefficient (0.3456666667). Square it (0.1194854445) and add it to both sides. Add '0.1194854445' to each side of the equation. 0.6913333333x + 0.1194854445 + x2 = 0.116 + 0.1194854445 Reorder the terms: 0.1194854445 + 0.6913333333x + x2 = 0.116 + 0.1194854445 Combine like terms: 0.116 + 0.1194854445 = 0.2354854445 0.1194854445 + 0.6913333333x + x2 = 0.2354854445 Factor a perfect square on the left side: (x + 0.3456666667)(x + 0.3456666667) = 0.2354854445 Calculate the square root of the right side: 0.485268425 Break this problem into two subproblems by setting (x + 0.3456666667) equal to 0.485268425 and -0.485268425.Subproblem 1
x + 0.3456666667 = 0.485268425 Simplifying x + 0.3456666667 = 0.485268425 Reorder the terms: 0.3456666667 + x = 0.485268425 Solving 0.3456666667 + x = 0.485268425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3456666667' to each side of the equation. 0.3456666667 + -0.3456666667 + x = 0.485268425 + -0.3456666667 Combine like terms: 0.3456666667 + -0.3456666667 = 0.0000000000 0.0000000000 + x = 0.485268425 + -0.3456666667 x = 0.485268425 + -0.3456666667 Combine like terms: 0.485268425 + -0.3456666667 = 0.1396017583 x = 0.1396017583 Simplifying x = 0.1396017583Subproblem 2
x + 0.3456666667 = -0.485268425 Simplifying x + 0.3456666667 = -0.485268425 Reorder the terms: 0.3456666667 + x = -0.485268425 Solving 0.3456666667 + x = -0.485268425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3456666667' to each side of the equation. 0.3456666667 + -0.3456666667 + x = -0.485268425 + -0.3456666667 Combine like terms: 0.3456666667 + -0.3456666667 = 0.0000000000 0.0000000000 + x = -0.485268425 + -0.3456666667 x = -0.485268425 + -0.3456666667 Combine like terms: -0.485268425 + -0.3456666667 = -0.8309350917 x = -0.8309350917 Simplifying x = -0.8309350917Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1396017583, -0.8309350917}
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