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Simplifying (x2) = (0.14 + -1x)(0.000046) x2 = (0.14 + -1x)(0.000046) Reorder the terms for easier multiplication: x2 = 0.000046(0.14 + -1x) x2 = (0.14 * 0.000046 + -1x * 0.000046) x2 = (0.00000644 + -0.000046x) Solving x2 = 0.00000644 + -0.000046x Solving for variable 'x'. Reorder the terms: -0.00000644 + 0.000046x + x2 = 0.00000644 + -0.000046x + -0.00000644 + 0.000046x Reorder the terms: -0.00000644 + 0.000046x + x2 = 0.00000644 + -0.00000644 + -0.000046x + 0.000046x Combine like terms: 0.00000644 + -0.00000644 = 0.00000000 -0.00000644 + 0.000046x + x2 = 0.00000000 + -0.000046x + 0.000046x -0.00000644 + 0.000046x + x2 = -0.000046x + 0.000046x Combine like terms: -0.000046x + 0.000046x = 0.000000 -0.00000644 + 0.000046x + x2 = 0.000000 Begin completing the square. Move the constant term to the right: Add '0.00000644' to each side of the equation. -0.00000644 + 0.000046x + 0.00000644 + x2 = 0.000000 + 0.00000644 Reorder the terms: -0.00000644 + 0.00000644 + 0.000046x + x2 = 0.000000 + 0.00000644 Combine like terms: -0.00000644 + 0.00000644 = 0.00000000 0.00000000 + 0.000046x + x2 = 0.000000 + 0.00000644 0.000046x + x2 = 0.000000 + 0.00000644 Combine like terms: 0.000000 + 0.00000644 = 0.00000644 0.000046x + x2 = 0.00000644 The x term is 0.000046x. Take half its coefficient (0.000023). Square it (0.000000000529) and add it to both sides. Add '0.000000000529' to each side of the equation. 0.000046x + 0.000000000529 + x2 = 0.00000644 + 0.000000000529 Reorder the terms: 0.000000000529 + 0.000046x + x2 = 0.00000644 + 0.000000000529 Combine like terms: 0.00000644 + 0.000000000529 = 0.000006440529 0.000000000529 + 0.000046x + x2 = 0.000006440529 Factor a perfect square on the left side: (x + 0.000023)(x + 0.000023) = 0.000006440529 Calculate the square root of the right side: 0.00253782 Break this problem into two subproblems by setting (x + 0.000023) equal to 0.00253782 and -0.00253782.Subproblem 1
x + 0.000023 = 0.00253782 Simplifying x + 0.000023 = 0.00253782 Reorder the terms: 0.000023 + x = 0.00253782 Solving 0.000023 + x = 0.00253782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000023' to each side of the equation. 0.000023 + -0.000023 + x = 0.00253782 + -0.000023 Combine like terms: 0.000023 + -0.000023 = 0.000000 0.000000 + x = 0.00253782 + -0.000023 x = 0.00253782 + -0.000023 Combine like terms: 0.00253782 + -0.000023 = 0.00251482 x = 0.00251482 Simplifying x = 0.00251482Subproblem 2
x + 0.000023 = -0.00253782 Simplifying x + 0.000023 = -0.00253782 Reorder the terms: 0.000023 + x = -0.00253782 Solving 0.000023 + x = -0.00253782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000023' to each side of the equation. 0.000023 + -0.000023 + x = -0.00253782 + -0.000023 Combine like terms: 0.000023 + -0.000023 = 0.000000 0.000000 + x = -0.00253782 + -0.000023 x = -0.00253782 + -0.000023 Combine like terms: -0.00253782 + -0.000023 = -0.00256082 x = -0.00256082 Simplifying x = -0.00256082Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00251482, -0.00256082}
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