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Simplifying 2x2 = 3.6x + 2.6 Reorder the terms: 2x2 = 2.6 + 3.6x Solving 2x2 = 2.6 + 3.6x Solving for variable 'x'. Reorder the terms: -2.6 + -3.6x + 2x2 = 2.6 + 3.6x + -2.6 + -3.6x Reorder the terms: -2.6 + -3.6x + 2x2 = 2.6 + -2.6 + 3.6x + -3.6x Combine like terms: 2.6 + -2.6 = 0.0 -2.6 + -3.6x + 2x2 = 0.0 + 3.6x + -3.6x -2.6 + -3.6x + 2x2 = 3.6x + -3.6x Combine like terms: 3.6x + -3.6x = 0.0 -2.6 + -3.6x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.3 + -1.8x + x2 = 0.0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -1.8x + 1.3 + x2 = 0.0 + 1.3 Reorder the terms: -1.3 + 1.3 + -1.8x + x2 = 0.0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -1.8x + x2 = 0.0 + 1.3 -1.8x + x2 = 0.0 + 1.3 Combine like terms: 0.0 + 1.3 = 1.3 -1.8x + x2 = 1.3 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 1.3 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 1.3 + 0.81 Combine like terms: 1.3 + 0.81 = 2.11 0.81 + -1.8x + x2 = 2.11 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 2.11 Calculate the square root of the right side: 1.452583905 Break this problem into two subproblems by setting (x + -0.9) equal to 1.452583905 and -1.452583905.Subproblem 1
x + -0.9 = 1.452583905 Simplifying x + -0.9 = 1.452583905 Reorder the terms: -0.9 + x = 1.452583905 Solving -0.9 + x = 1.452583905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 1.452583905 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 1.452583905 + 0.9 x = 1.452583905 + 0.9 Combine like terms: 1.452583905 + 0.9 = 2.352583905 x = 2.352583905 Simplifying x = 2.352583905Subproblem 2
x + -0.9 = -1.452583905 Simplifying x + -0.9 = -1.452583905 Reorder the terms: -0.9 + x = -1.452583905 Solving -0.9 + x = -1.452583905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -1.452583905 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -1.452583905 + 0.9 x = -1.452583905 + 0.9 Combine like terms: -1.452583905 + 0.9 = -0.552583905 x = -0.552583905 Simplifying x = -0.552583905Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.352583905, -0.552583905}
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