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Simplifying 1000000x2 + 20x + -2 = 0 Reorder the terms: -2 + 20x + 1000000x2 = 0 Solving -2 + 20x + 1000000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 10x + 500000x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 10x + 500000x2)' equal to zero and attempt to solve: Simplifying -1 + 10x + 500000x2 = 0 Solving -1 + 10x + 500000x2 = 0 Begin completing the square. Divide all terms by 500000 the coefficient of the squared term: Divide each side by '500000'. -0.000002 + 0.00002x + x2 = 0.00000 Move the constant term to the right: Add '0.000002' to each side of the equation. -0.000002 + 0.00002x + 0.000002 + x2 = 0.00000 + 0.000002 Reorder the terms: -0.000002 + 0.000002 + 0.00002x + x2 = 0.00000 + 0.000002 Combine like terms: -0.000002 + 0.000002 = 0.000000 0.000000 + 0.00002x + x2 = 0.00000 + 0.000002 0.00002x + x2 = 0.00000 + 0.000002 Combine like terms: 0.00000 + 0.000002 = 0.000002 0.00002x + x2 = 0.000002 The x term is 0.00002x. Take half its coefficient (0.00001). Square it (0.0000000001) and add it to both sides. Add '0.0000000001' to each side of the equation. 0.00002x + 0.0000000001 + x2 = 0.000002 + 0.0000000001 Reorder the terms: 0.0000000001 + 0.00002x + x2 = 0.000002 + 0.0000000001 Combine like terms: 0.000002 + 0.0000000001 = 0.0000020001 0.0000000001 + 0.00002x + x2 = 0.0000020001 Factor a perfect square on the left side: (x + 0.00001)(x + 0.00001) = 0.0000020001 Calculate the square root of the right side: 0.001414249 Break this problem into two subproblems by setting (x + 0.00001) equal to 0.001414249 and -0.001414249.Subproblem 1
x + 0.00001 = 0.001414249 Simplifying x + 0.00001 = 0.001414249 Reorder the terms: 0.00001 + x = 0.001414249 Solving 0.00001 + x = 0.001414249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00001' to each side of the equation. 0.00001 + -0.00001 + x = 0.001414249 + -0.00001 Combine like terms: 0.00001 + -0.00001 = 0.00000 0.00000 + x = 0.001414249 + -0.00001 x = 0.001414249 + -0.00001 Combine like terms: 0.001414249 + -0.00001 = 0.001404249 x = 0.001404249 Simplifying x = 0.001404249Subproblem 2
x + 0.00001 = -0.001414249 Simplifying x + 0.00001 = -0.001414249 Reorder the terms: 0.00001 + x = -0.001414249 Solving 0.00001 + x = -0.001414249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00001' to each side of the equation. 0.00001 + -0.00001 + x = -0.001414249 + -0.00001 Combine like terms: 0.00001 + -0.00001 = 0.00000 0.00000 + x = -0.001414249 + -0.00001 x = -0.001414249 + -0.00001 Combine like terms: -0.001414249 + -0.00001 = -0.001424249 x = -0.001424249 Simplifying x = -0.001424249Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.001404249, -0.001424249}Solution
x = {0.001404249, -0.001424249}
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