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Simplifying x2 + -0.1x + -1.7 = 0 Reorder the terms: -1.7 + -0.1x + x2 = 0 Solving -1.7 + -0.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + -0.1x + 1.7 + x2 = 0 + 1.7 Reorder the terms: -1.7 + 1.7 + -0.1x + x2 = 0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + -0.1x + x2 = 0 + 1.7 -0.1x + x2 = 0 + 1.7 Combine like terms: 0 + 1.7 = 1.7 -0.1x + x2 = 1.7 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 1.7 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 1.7 + 0.0025 Combine like terms: 1.7 + 0.0025 = 1.7025 0.0025 + -0.1x + x2 = 1.7025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 1.7025 Calculate the square root of the right side: 1.304798835 Break this problem into two subproblems by setting (x + -0.05) equal to 1.304798835 and -1.304798835.Subproblem 1
x + -0.05 = 1.304798835 Simplifying x + -0.05 = 1.304798835 Reorder the terms: -0.05 + x = 1.304798835 Solving -0.05 + x = 1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 1.304798835 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 1.304798835 + 0.05 x = 1.304798835 + 0.05 Combine like terms: 1.304798835 + 0.05 = 1.354798835 x = 1.354798835 Simplifying x = 1.354798835Subproblem 2
x + -0.05 = -1.304798835 Simplifying x + -0.05 = -1.304798835 Reorder the terms: -0.05 + x = -1.304798835 Solving -0.05 + x = -1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -1.304798835 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -1.304798835 + 0.05 x = -1.304798835 + 0.05 Combine like terms: -1.304798835 + 0.05 = -1.254798835 x = -1.254798835 Simplifying x = -1.254798835Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.354798835, -1.254798835}
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