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Simplifying x2 + -0.018x + -0.063 = 0 Reorder the terms: -0.063 + -0.018x + x2 = 0 Solving -0.063 + -0.018x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.063' to each side of the equation. -0.063 + -0.018x + 0.063 + x2 = 0 + 0.063 Reorder the terms: -0.063 + 0.063 + -0.018x + x2 = 0 + 0.063 Combine like terms: -0.063 + 0.063 = 0.000 0.000 + -0.018x + x2 = 0 + 0.063 -0.018x + x2 = 0 + 0.063 Combine like terms: 0 + 0.063 = 0.063 -0.018x + x2 = 0.063 The x term is -0.018x. Take half its coefficient (-0.009). Square it (0.000081) and add it to both sides. Add '0.000081' to each side of the equation. -0.018x + 0.000081 + x2 = 0.063 + 0.000081 Reorder the terms: 0.000081 + -0.018x + x2 = 0.063 + 0.000081 Combine like terms: 0.063 + 0.000081 = 0.063081 0.000081 + -0.018x + x2 = 0.063081 Factor a perfect square on the left side: (x + -0.009)(x + -0.009) = 0.063081 Calculate the square root of the right side: 0.251159312 Break this problem into two subproblems by setting (x + -0.009) equal to 0.251159312 and -0.251159312.Subproblem 1
x + -0.009 = 0.251159312 Simplifying x + -0.009 = 0.251159312 Reorder the terms: -0.009 + x = 0.251159312 Solving -0.009 + x = 0.251159312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.009' to each side of the equation. -0.009 + 0.009 + x = 0.251159312 + 0.009 Combine like terms: -0.009 + 0.009 = 0.000 0.000 + x = 0.251159312 + 0.009 x = 0.251159312 + 0.009 Combine like terms: 0.251159312 + 0.009 = 0.260159312 x = 0.260159312 Simplifying x = 0.260159312Subproblem 2
x + -0.009 = -0.251159312 Simplifying x + -0.009 = -0.251159312 Reorder the terms: -0.009 + x = -0.251159312 Solving -0.009 + x = -0.251159312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.009' to each side of the equation. -0.009 + 0.009 + x = -0.251159312 + 0.009 Combine like terms: -0.009 + 0.009 = 0.000 0.000 + x = -0.251159312 + 0.009 x = -0.251159312 + 0.009 Combine like terms: -0.251159312 + 0.009 = -0.242159312 x = -0.242159312 Simplifying x = -0.242159312Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.260159312, -0.242159312}
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