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Simplifying x2 + 0.028x = 0.0000000000005 Reorder the terms: 0.028x + x2 = 0.0000000000005 Solving 0.028x + x2 = 0.0000000000005 Solving for variable 'x'. Reorder the terms: -0.0000000000005 + 0.028x + x2 = 0.0000000000005 + -0.0000000000005 Combine like terms: 0.0000000000005 + -0.0000000000005 = 0.0000000000000 -0.0000000000005 + 0.028x + x2 = 0.0000000000000 Begin completing the square. Move the constant term to the right: Add '0.0000000000005' to each side of the equation. -0.0000000000005 + 0.028x + 0.0000000000005 + x2 = 0.0000000000000 + 0.0000000000005 Reorder the terms: -0.0000000000005 + 0.0000000000005 + 0.028x + x2 = 0.0000000000000 + 0.0000000000005 Combine like terms: -0.0000000000005 + 0.0000000000005 = 0.0000000000000 0.0000000000000 + 0.028x + x2 = 0.0000000000000 + 0.0000000000005 0.028x + x2 = 0.0000000000000 + 0.0000000000005 Combine like terms: 0.0000000000000 + 0.0000000000005 = 0.0000000000005 0.028x + x2 = 0.0000000000005 The x term is 0.028x. Take half its coefficient (0.014). Square it (0.000196) and add it to both sides. Add '0.000196' to each side of the equation. 0.028x + 0.000196 + x2 = 0.0000000000005 + 0.000196 Reorder the terms: 0.000196 + 0.028x + x2 = 0.0000000000005 + 0.000196 Combine like terms: 0.0000000000005 + 0.000196 = 0.0001960000005 0.000196 + 0.028x + x2 = 0.0001960000005 Factor a perfect square on the left side: (x + 0.014)(x + 0.014) = 0.0001960000005 Calculate the square root of the right side: 0.014 Break this problem into two subproblems by setting (x + 0.014) equal to 0.014 and -0.014.Subproblem 1
x + 0.014 = 0.014 Simplifying x + 0.014 = 0.014 Reorder the terms: 0.014 + x = 0.014 Add '-0.014' to each side of the equation. 0.014 + -0.014 + x = 0.014 + -0.014 Combine like terms: 0.014 + -0.014 = 0.000 0.000 + x = 0.014 + -0.014 x = 0.014 + -0.014 Combine like terms: 0.014 + -0.014 = 0.000 x = 0.000 Solving x = 0.000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Simplifying x = 0.000Subproblem 2
x + 0.014 = -0.014 Simplifying x + 0.014 = -0.014 Reorder the terms: 0.014 + x = -0.014 Solving 0.014 + x = -0.014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.014' to each side of the equation. 0.014 + -0.014 + x = -0.014 + -0.014 Combine like terms: 0.014 + -0.014 = 0.000 0.000 + x = -0.014 + -0.014 x = -0.014 + -0.014 Combine like terms: -0.014 + -0.014 = -0.028 x = -0.028 Simplifying x = -0.028Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000, -0.028}
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