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Simplifying -2.3x2 + 4.6x + -2 = 0 Reorder the terms: -2 + 4.6x + -2.3x2 = 0 Solving -2 + 4.6x + -2.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.3 the coefficient of the squared term: Divide each side by '-2.3'. 0.8695652174 + -2x + x2 = 0 Move the constant term to the right: Add '-0.8695652174' to each side of the equation. 0.8695652174 + -2x + -0.8695652174 + x2 = 0 + -0.8695652174 Reorder the terms: 0.8695652174 + -0.8695652174 + -2x + x2 = 0 + -0.8695652174 Combine like terms: 0.8695652174 + -0.8695652174 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.8695652174 -2x + x2 = 0 + -0.8695652174 Combine like terms: 0 + -0.8695652174 = -0.8695652174 -2x + x2 = -0.8695652174 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 = -0.8695652174 + 1 Reorder the terms: 1 + -2x + x2 = -0.8695652174 + 1 Combine like terms: -0.8695652174 + 1 = 0.1304347826 1 + -2x + x2 = 0.1304347826 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.1304347826 Calculate the square root of the right side: 0.361157559 Break this problem into two subproblems by setting (x + -1) equal to 0.361157559 and -0.361157559.Subproblem 1
x + -1 = 0.361157559 Simplifying x + -1 = 0.361157559 Reorder the terms: -1 + x = 0.361157559 Solving -1 + x = 0.361157559 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 = 0.361157559 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.361157559 + 1 x = 0.361157559 + 1 Combine like terms: 0.361157559 + 1 = 1.361157559 x = 1.361157559 Simplifying x = 1.361157559Subproblem 2
x + -1 = -0.361157559 Simplifying x + -1 = -0.361157559 Reorder the terms: -1 + x = -0.361157559 Solving -1 + x = -0.361157559 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 = -0.361157559 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.361157559 + 1 x = -0.361157559 + 1 Combine like terms: -0.361157559 + 1 = 0.638842441 x = 0.638842441 Simplifying x = 0.638842441Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.361157559, 0.638842441}
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