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Simplifying x2 = 0.00135(1.1 + -1x) x2 = (1.1 * 0.00135 + -1x * 0.00135) x2 = (0.001485 + -0.00135x) Solving x2 = 0.001485 + -0.00135x Solving for variable 'x'. Reorder the terms: -0.001485 + 0.00135x + x2 = 0.001485 + -0.00135x + -0.001485 + 0.00135x Reorder the terms: -0.001485 + 0.00135x + x2 = 0.001485 + -0.001485 + -0.00135x + 0.00135x Combine like terms: 0.001485 + -0.001485 = 0.000000 -0.001485 + 0.00135x + x2 = 0.000000 + -0.00135x + 0.00135x -0.001485 + 0.00135x + x2 = -0.00135x + 0.00135x Combine like terms: -0.00135x + 0.00135x = 0.00000 -0.001485 + 0.00135x + x2 = 0.00000 Begin completing the square. Move the constant term to the right: Add '0.001485' to each side of the equation. -0.001485 + 0.00135x + 0.001485 + x2 = 0.00000 + 0.001485 Reorder the terms: -0.001485 + 0.001485 + 0.00135x + x2 = 0.00000 + 0.001485 Combine like terms: -0.001485 + 0.001485 = 0.000000 0.000000 + 0.00135x + x2 = 0.00000 + 0.001485 0.00135x + x2 = 0.00000 + 0.001485 Combine like terms: 0.00000 + 0.001485 = 0.001485 0.00135x + x2 = 0.001485 The x term is 0.00135x. Take half its coefficient (0.000675). Square it (0.000000455625) and add it to both sides. Add '0.000000455625' to each side of the equation. 0.00135x + 0.000000455625 + x2 = 0.001485 + 0.000000455625 Reorder the terms: 0.000000455625 + 0.00135x + x2 = 0.001485 + 0.000000455625 Combine like terms: 0.001485 + 0.000000455625 = 0.001485455625 0.000000455625 + 0.00135x + x2 = 0.001485455625 Factor a perfect square on the left side: (x + 0.000675)(x + 0.000675) = 0.001485455625 Calculate the square root of the right side: 0.038541609 Break this problem into two subproblems by setting (x + 0.000675) equal to 0.038541609 and -0.038541609.Subproblem 1
x + 0.000675 = 0.038541609 Simplifying x + 0.000675 = 0.038541609 Reorder the terms: 0.000675 + x = 0.038541609 Solving 0.000675 + x = 0.038541609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000675' to each side of the equation. 0.000675 + -0.000675 + x = 0.038541609 + -0.000675 Combine like terms: 0.000675 + -0.000675 = 0.000000 0.000000 + x = 0.038541609 + -0.000675 x = 0.038541609 + -0.000675 Combine like terms: 0.038541609 + -0.000675 = 0.037866609 x = 0.037866609 Simplifying x = 0.037866609Subproblem 2
x + 0.000675 = -0.038541609 Simplifying x + 0.000675 = -0.038541609 Reorder the terms: 0.000675 + x = -0.038541609 Solving 0.000675 + x = -0.038541609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000675' to each side of the equation. 0.000675 + -0.000675 + x = -0.038541609 + -0.000675 Combine like terms: 0.000675 + -0.000675 = 0.000000 0.000000 + x = -0.038541609 + -0.000675 x = -0.038541609 + -0.000675 Combine like terms: -0.038541609 + -0.000675 = -0.039216609 x = -0.039216609 Simplifying x = -0.039216609Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.037866609, -0.039216609}
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