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Simplifying x2 + 1.67x + -14.8346 = 0 Reorder the terms: -14.8346 + 1.67x + x2 = 0 Solving -14.8346 + 1.67x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '14.8346' to each side of the equation. -14.8346 + 1.67x + 14.8346 + x2 = 0 + 14.8346 Reorder the terms: -14.8346 + 14.8346 + 1.67x + x2 = 0 + 14.8346 Combine like terms: -14.8346 + 14.8346 = 0.0000 0.0000 + 1.67x + x2 = 0 + 14.8346 1.67x + x2 = 0 + 14.8346 Combine like terms: 0 + 14.8346 = 14.8346 1.67x + x2 = 14.8346 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 = 14.8346 + 0.697225 Reorder the terms: 0.697225 + 1.67x + x2 = 14.8346 + 0.697225 Combine like terms: 14.8346 + 0.697225 = 15.531825 0.697225 + 1.67x + x2 = 15.531825 Factor a perfect square on the left side: (x + 0.835)(x + 0.835) = 15.531825 Calculate the square root of the right side: 3.941043644 Break this problem into two subproblems by setting (x + 0.835) equal to 3.941043644 and -3.941043644.Subproblem 1
x + 0.835 = 3.941043644 Simplifying x + 0.835 = 3.941043644 Reorder the terms: 0.835 + x = 3.941043644 Solving 0.835 + x = 3.941043644 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 = 3.941043644 + -0.835 Combine like terms: 0.835 + -0.835 = 0.000 0.000 + x = 3.941043644 + -0.835 x = 3.941043644 + -0.835 Combine like terms: 3.941043644 + -0.835 = 3.106043644 x = 3.106043644 Simplifying x = 3.106043644Subproblem 2
x + 0.835 = -3.941043644 Simplifying x + 0.835 = -3.941043644 Reorder the terms: 0.835 + x = -3.941043644 Solving 0.835 + x = -3.941043644 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 = -3.941043644 + -0.835 Combine like terms: 0.835 + -0.835 = 0.000 0.000 + x = -3.941043644 + -0.835 x = -3.941043644 + -0.835 Combine like terms: -3.941043644 + -0.835 = -4.776043644 x = -4.776043644 Simplifying x = -4.776043644Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.106043644, -4.776043644}
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