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Simplifying x2 + 1.67x + -10.296 = 0 Reorder the terms: -10.296 + 1.67x + x2 = 0 Solving -10.296 + 1.67x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10.296' to each side of the equation. -10.296 + 1.67x + 10.296 + x2 = 0 + 10.296 Reorder the terms: -10.296 + 10.296 + 1.67x + x2 = 0 + 10.296 Combine like terms: -10.296 + 10.296 = 0.000 0.000 + 1.67x + x2 = 0 + 10.296 1.67x + x2 = 0 + 10.296 Combine like terms: 0 + 10.296 = 10.296 1.67x + x2 = 10.296 The x term is 1.67x. Take half its coefficient (0.835). Square it (0.697225) and add it to both sides. Add '0.697225' to each side of the equation. 1.67x + 0.697225 + x2 = 10.296 + 0.697225 Reorder the terms: 0.697225 + 1.67x + x2 = 10.296 + 0.697225 Combine like terms: 10.296 + 0.697225 = 10.993225 0.697225 + 1.67x + x2 = 10.993225 Factor a perfect square on the left side: (x + 0.835)(x + 0.835) = 10.993225 Calculate the square root of the right side: 3.315603263 Break this problem into two subproblems by setting (x + 0.835) equal to 3.315603263 and -3.315603263.Subproblem 1
x + 0.835 = 3.315603263 Simplifying x + 0.835 = 3.315603263 Reorder the terms: 0.835 + x = 3.315603263 Solving 0.835 + x = 3.315603263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.835' to each side of the equation. 0.835 + -0.835 + x = 3.315603263 + -0.835 Combine like terms: 0.835 + -0.835 = 0.000 0.000 + x = 3.315603263 + -0.835 x = 3.315603263 + -0.835 Combine like terms: 3.315603263 + -0.835 = 2.480603263 x = 2.480603263 Simplifying x = 2.480603263Subproblem 2
x + 0.835 = -3.315603263 Simplifying x + 0.835 = -3.315603263 Reorder the terms: 0.835 + x = -3.315603263 Solving 0.835 + x = -3.315603263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.835' to each side of the equation. 0.835 + -0.835 + x = -3.315603263 + -0.835 Combine like terms: 0.835 + -0.835 = 0.000 0.000 + x = -3.315603263 + -0.835 x = -3.315603263 + -0.835 Combine like terms: -3.315603263 + -0.835 = -4.150603263 x = -4.150603263 Simplifying x = -4.150603263Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.480603263, -4.150603263}
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