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Simplifying 0.66x2 + -2.33x + 1 = 0 Reorder the terms: 1 + -2.33x + 0.66x2 = 0 Solving 1 + -2.33x + 0.66x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.66 the coefficient of the squared term: Divide each side by '0.66'. 1.515151515 + -3.53030303x + x2 = 0 Move the constant term to the right: Add '-1.515151515' to each side of the equation. 1.515151515 + -3.53030303x + -1.515151515 + x2 = 0 + -1.515151515 Reorder the terms: 1.515151515 + -1.515151515 + -3.53030303x + x2 = 0 + -1.515151515 Combine like terms: 1.515151515 + -1.515151515 = 0.000000000 0.000000000 + -3.53030303x + x2 = 0 + -1.515151515 -3.53030303x + x2 = 0 + -1.515151515 Combine like terms: 0 + -1.515151515 = -1.515151515 -3.53030303x + x2 = -1.515151515 The x term is -3.53030303x. Take half its coefficient (-1.765151515). Square it (3.115759871) and add it to both sides. Add '3.115759871' to each side of the equation. -3.53030303x + 3.115759871 + x2 = -1.515151515 + 3.115759871 Reorder the terms: 3.115759871 + -3.53030303x + x2 = -1.515151515 + 3.115759871 Combine like terms: -1.515151515 + 3.115759871 = 1.600608356 3.115759871 + -3.53030303x + x2 = 1.600608356 Factor a perfect square on the left side: (x + -1.765151515)(x + -1.765151515) = 1.600608356 Calculate the square root of the right side: 1.265151515 Break this problem into two subproblems by setting (x + -1.765151515) equal to 1.265151515 and -1.265151515.Subproblem 1
x + -1.765151515 = 1.265151515 Simplifying x + -1.765151515 = 1.265151515 Reorder the terms: -1.765151515 + x = 1.265151515 Solving -1.765151515 + x = 1.265151515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.765151515' to each side of the equation. -1.765151515 + 1.765151515 + x = 1.265151515 + 1.765151515 Combine like terms: -1.765151515 + 1.765151515 = 0.000000000 0.000000000 + x = 1.265151515 + 1.765151515 x = 1.265151515 + 1.765151515 Combine like terms: 1.265151515 + 1.765151515 = 3.03030303 x = 3.03030303 Simplifying x = 3.03030303Subproblem 2
x + -1.765151515 = -1.265151515 Simplifying x + -1.765151515 = -1.265151515 Reorder the terms: -1.765151515 + x = -1.265151515 Solving -1.765151515 + x = -1.265151515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.765151515' to each side of the equation. -1.765151515 + 1.765151515 + x = -1.265151515 + 1.765151515 Combine like terms: -1.765151515 + 1.765151515 = 0.000000000 0.000000000 + x = -1.265151515 + 1.765151515 x = -1.265151515 + 1.765151515 Combine like terms: -1.265151515 + 1.765151515 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.03030303, 0.5}
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