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Simplifying 0 = -0.6x2 + 1.2x + 1.7 Reorder the terms: 0 = 1.7 + 1.2x + -0.6x2 Solving 0 = 1.7 + 1.2x + -0.6x2 Solving for variable 'x'. Combine like terms: 0 + -1.7 = -1.7 -1.7 + -1.2x + 0.6x2 = 1.7 + 1.2x + -0.6x2 + -1.7 + -1.2x + 0.6x2 Reorder the terms: -1.7 + -1.2x + 0.6x2 = 1.7 + -1.7 + 1.2x + -1.2x + -0.6x2 + 0.6x2 Combine like terms: 1.7 + -1.7 = 0.0 -1.7 + -1.2x + 0.6x2 = 0.0 + 1.2x + -1.2x + -0.6x2 + 0.6x2 -1.7 + -1.2x + 0.6x2 = 1.2x + -1.2x + -0.6x2 + 0.6x2 Combine like terms: 1.2x + -1.2x = 0.0 -1.7 + -1.2x + 0.6x2 = 0.0 + -0.6x2 + 0.6x2 -1.7 + -1.2x + 0.6x2 = -0.6x2 + 0.6x2 Combine like terms: -0.6x2 + 0.6x2 = 0.0 -1.7 + -1.2x + 0.6x2 = 0.0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -2.833333333 + -2x + x2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + -2x + 2.833333333 + x2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + -2x + x2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 2.833333333 -2x + x2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 -2x + x2 = 2.833333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 2.833333333 + 1 Reorder the terms: 1 + -2x + x2 = 2.833333333 + 1 Combine like terms: 2.833333333 + 1 = 3.833333333 1 + -2x + x2 = 3.833333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.833333333 Calculate the square root of the right side: 1.957890021 Break this problem into two subproblems by setting (x + -1) equal to 1.957890021 and -1.957890021.Subproblem 1
x + -1 = 1.957890021 Simplifying x + -1 = 1.957890021 Reorder the terms: -1 + x = 1.957890021 Solving -1 + x = 1.957890021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.957890021 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.957890021 + 1 x = 1.957890021 + 1 Combine like terms: 1.957890021 + 1 = 2.957890021 x = 2.957890021 Simplifying x = 2.957890021Subproblem 2
x + -1 = -1.957890021 Simplifying x + -1 = -1.957890021 Reorder the terms: -1 + x = -1.957890021 Solving -1 + x = -1.957890021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.957890021 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.957890021 + 1 x = -1.957890021 + 1 Combine like terms: -1.957890021 + 1 = -0.957890021 x = -0.957890021 Simplifying x = -0.957890021Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.957890021, -0.957890021}
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