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Simplifying 1.2x2 + -1.7x + 0.6 = 0 Reorder the terms: 0.6 + -1.7x + 1.2x2 = 0 Solving 0.6 + -1.7x + 1.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.2 the coefficient of the squared term: Divide each side by '1.2'. 0.5 + -1.416666667x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.416666667x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.416666667x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.416666667x + x2 = 0 + -0.5 -1.416666667x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.416666667x + x2 = -0.5 The x term is -1.416666667x. Take half its coefficient (-0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. -1.416666667x + 0.5017361113 + x2 = -0.5 + 0.5017361113 Reorder the terms: 0.5017361113 + -1.416666667x + x2 = -0.5 + 0.5017361113 Combine like terms: -0.5 + 0.5017361113 = 0.0017361113 0.5017361113 + -1.416666667x + x2 = 0.0017361113 Factor a perfect square on the left side: (x + -0.7083333335)(x + -0.7083333335) = 0.0017361113 Calculate the square root of the right side: 0.041666669 Break this problem into two subproblems by setting (x + -0.7083333335) equal to 0.041666669 and -0.041666669.Subproblem 1
x + -0.7083333335 = 0.041666669 Simplifying x + -0.7083333335 = 0.041666669 Reorder the terms: -0.7083333335 + x = 0.041666669 Solving -0.7083333335 + x = 0.041666669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = 0.041666669 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = 0.041666669 + 0.7083333335 x = 0.041666669 + 0.7083333335 Combine like terms: 0.041666669 + 0.7083333335 = 0.7500000025 x = 0.7500000025 Simplifying x = 0.7500000025Subproblem 2
x + -0.7083333335 = -0.041666669 Simplifying x + -0.7083333335 = -0.041666669 Reorder the terms: -0.7083333335 + x = -0.041666669 Solving -0.7083333335 + x = -0.041666669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = -0.041666669 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = -0.041666669 + 0.7083333335 x = -0.041666669 + 0.7083333335 Combine like terms: -0.041666669 + 0.7083333335 = 0.6666666645 x = 0.6666666645 Simplifying x = 0.6666666645Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7500000025, 0.6666666645}
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