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Simplifying 0.00004 + -0.0004x + -4x2 = 0 Solving 0.00004 + -0.0004x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.00001 + 0.0001x + x2 = 0 Move the constant term to the right: Add '0.00001' to each side of the equation. -0.00001 + 0.0001x + 0.00001 + x2 = 0 + 0.00001 Reorder the terms: -0.00001 + 0.00001 + 0.0001x + x2 = 0 + 0.00001 Combine like terms: -0.00001 + 0.00001 = 0.00000 0.00000 + 0.0001x + x2 = 0 + 0.00001 0.0001x + x2 = 0 + 0.00001 Combine like terms: 0 + 0.00001 = 0.00001 0.0001x + x2 = 0.00001 The x term is 0.0001x. Take half its coefficient (0.00005). Square it (0.0000000025) and add it to both sides. Add '0.0000000025' to each side of the equation. 0.0001x + 0.0000000025 + x2 = 0.00001 + 0.0000000025 Reorder the terms: 0.0000000025 + 0.0001x + x2 = 0.00001 + 0.0000000025 Combine like terms: 0.00001 + 0.0000000025 = 0.0000100025 0.0000000025 + 0.0001x + x2 = 0.0000100025 Factor a perfect square on the left side: (x + 0.00005)(x + 0.00005) = 0.0000100025 Calculate the square root of the right side: 0.003162673 Break this problem into two subproblems by setting (x + 0.00005) equal to 0.003162673 and -0.003162673.Subproblem 1
x + 0.00005 = 0.003162673 Simplifying x + 0.00005 = 0.003162673 Reorder the terms: 0.00005 + x = 0.003162673 Solving 0.00005 + x = 0.003162673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00005' to each side of the equation. 0.00005 + -0.00005 + x = 0.003162673 + -0.00005 Combine like terms: 0.00005 + -0.00005 = 0.00000 0.00000 + x = 0.003162673 + -0.00005 x = 0.003162673 + -0.00005 Combine like terms: 0.003162673 + -0.00005 = 0.003112673 x = 0.003112673 Simplifying x = 0.003112673Subproblem 2
x + 0.00005 = -0.003162673 Simplifying x + 0.00005 = -0.003162673 Reorder the terms: 0.00005 + x = -0.003162673 Solving 0.00005 + x = -0.003162673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00005' to each side of the equation. 0.00005 + -0.00005 + x = -0.003162673 + -0.00005 Combine like terms: 0.00005 + -0.00005 = 0.00000 0.00000 + x = -0.003162673 + -0.00005 x = -0.003162673 + -0.00005 Combine like terms: -0.003162673 + -0.00005 = -0.003212673 x = -0.003212673 Simplifying x = -0.003212673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.003112673, -0.003212673}
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