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Simplifying (0.1 + -1x)(0.0000833) = x2 Reorder the terms for easier multiplication: 0.0000833(0.1 + -1x) = x2 (0.1 * 0.0000833 + -1x * 0.0000833) = x2 (0.00000833 + -0.0000833x) = x2 Solving 0.00000833 + -0.0000833x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.00000833 + -0.0000833x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.00000833 + 0.0000833x + x2 = 0 Move the constant term to the right: Add '0.00000833' to each side of the equation. -0.00000833 + 0.0000833x + 0.00000833 + x2 = 0 + 0.00000833 Reorder the terms: -0.00000833 + 0.00000833 + 0.0000833x + x2 = 0 + 0.00000833 Combine like terms: -0.00000833 + 0.00000833 = 0.00000000 0.00000000 + 0.0000833x + x2 = 0 + 0.00000833 0.0000833x + x2 = 0 + 0.00000833 Combine like terms: 0 + 0.00000833 = 0.00000833 0.0000833x + x2 = 0.00000833 The x term is 0.0000833x. Take half its coefficient (0.00004165). Square it (0.0000000017347225) and add it to both sides. Add '0.0000000017347225' to each side of the equation. 0.0000833x + 0.0000000017347225 + x2 = 0.00000833 + 0.0000000017347225 Reorder the terms: 0.0000000017347225 + 0.0000833x + x2 = 0.00000833 + 0.0000000017347225 Combine like terms: 0.00000833 + 0.0000000017347225 = 0.0000083317347225 0.0000000017347225 + 0.0000833x + x2 = 0.0000083317347225 Factor a perfect square on the left side: (x + 0.00004165)(x + 0.00004165) = 0.0000083317347225 Calculate the square root of the right side: 0.002886474 Break this problem into two subproblems by setting (x + 0.00004165) equal to 0.002886474 and -0.002886474.Subproblem 1
x + 0.00004165 = 0.002886474 Simplifying x + 0.00004165 = 0.002886474 Reorder the terms: 0.00004165 + x = 0.002886474 Solving 0.00004165 + x = 0.002886474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00004165' to each side of the equation. 0.00004165 + -0.00004165 + x = 0.002886474 + -0.00004165 Combine like terms: 0.00004165 + -0.00004165 = 0.00000000 0.00000000 + x = 0.002886474 + -0.00004165 x = 0.002886474 + -0.00004165 Combine like terms: 0.002886474 + -0.00004165 = 0.002844824 x = 0.002844824 Simplifying x = 0.002844824Subproblem 2
x + 0.00004165 = -0.002886474 Simplifying x + 0.00004165 = -0.002886474 Reorder the terms: 0.00004165 + x = -0.002886474 Solving 0.00004165 + x = -0.002886474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00004165' to each side of the equation. 0.00004165 + -0.00004165 + x = -0.002886474 + -0.00004165 Combine like terms: 0.00004165 + -0.00004165 = 0.00000000 0.00000000 + x = -0.002886474 + -0.00004165 x = -0.002886474 + -0.00004165 Combine like terms: -0.002886474 + -0.00004165 = -0.002928124 x = -0.002928124 Simplifying x = -0.002928124Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.002844824, -0.002928124}
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