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Simplifying x2 + -0.95x + -0.035 = 0 Reorder the terms: -0.035 + -0.95x + x2 = 0 Solving -0.035 + -0.95x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.035' to each side of the equation. -0.035 + -0.95x + 0.035 + x2 = 0 + 0.035 Reorder the terms: -0.035 + 0.035 + -0.95x + x2 = 0 + 0.035 Combine like terms: -0.035 + 0.035 = 0.000 0.000 + -0.95x + x2 = 0 + 0.035 -0.95x + x2 = 0 + 0.035 Combine like terms: 0 + 0.035 = 0.035 -0.95x + x2 = 0.035 The x term is -0.95x. Take half its coefficient (-0.475). Square it (0.225625) and add it to both sides. Add '0.225625' to each side of the equation. -0.95x + 0.225625 + x2 = 0.035 + 0.225625 Reorder the terms: 0.225625 + -0.95x + x2 = 0.035 + 0.225625 Combine like terms: 0.035 + 0.225625 = 0.260625 0.225625 + -0.95x + x2 = 0.260625 Factor a perfect square on the left side: (x + -0.475)(x + -0.475) = 0.260625 Calculate the square root of the right side: 0.510514446 Break this problem into two subproblems by setting (x + -0.475) equal to 0.510514446 and -0.510514446.Subproblem 1
x + -0.475 = 0.510514446 Simplifying x + -0.475 = 0.510514446 Reorder the terms: -0.475 + x = 0.510514446 Solving -0.475 + x = 0.510514446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.475' to each side of the equation. -0.475 + 0.475 + x = 0.510514446 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + x = 0.510514446 + 0.475 x = 0.510514446 + 0.475 Combine like terms: 0.510514446 + 0.475 = 0.985514446 x = 0.985514446 Simplifying x = 0.985514446Subproblem 2
x + -0.475 = -0.510514446 Simplifying x + -0.475 = -0.510514446 Reorder the terms: -0.475 + x = -0.510514446 Solving -0.475 + x = -0.510514446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.475' to each side of the equation. -0.475 + 0.475 + x = -0.510514446 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + x = -0.510514446 + 0.475 x = -0.510514446 + 0.475 Combine like terms: -0.510514446 + 0.475 = -0.035514446 x = -0.035514446 Simplifying x = -0.035514446Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.985514446, -0.035514446}
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