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Simplifying 0.124415 + -0.745x + -1x2 = 0 Solving 0.124415 + -0.745x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.124415 + 0.745x + x2 = 0 Move the constant term to the right: Add '0.124415' to each side of the equation. -0.124415 + 0.745x + 0.124415 + x2 = 0 + 0.124415 Reorder the terms: -0.124415 + 0.124415 + 0.745x + x2 = 0 + 0.124415 Combine like terms: -0.124415 + 0.124415 = 0.000000 0.000000 + 0.745x + x2 = 0 + 0.124415 0.745x + x2 = 0 + 0.124415 Combine like terms: 0 + 0.124415 = 0.124415 0.745x + x2 = 0.124415 The x term is 0.745x. Take half its coefficient (0.3725). Square it (0.13875625) and add it to both sides. Add '0.13875625' to each side of the equation. 0.745x + 0.13875625 + x2 = 0.124415 + 0.13875625 Reorder the terms: 0.13875625 + 0.745x + x2 = 0.124415 + 0.13875625 Combine like terms: 0.124415 + 0.13875625 = 0.26317125 0.13875625 + 0.745x + x2 = 0.26317125 Factor a perfect square on the left side: (x + 0.3725)(x + 0.3725) = 0.26317125 Calculate the square root of the right side: 0.513002193 Break this problem into two subproblems by setting (x + 0.3725) equal to 0.513002193 and -0.513002193.Subproblem 1
x + 0.3725 = 0.513002193 Simplifying x + 0.3725 = 0.513002193 Reorder the terms: 0.3725 + x = 0.513002193 Solving 0.3725 + x = 0.513002193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3725' to each side of the equation. 0.3725 + -0.3725 + x = 0.513002193 + -0.3725 Combine like terms: 0.3725 + -0.3725 = 0.0000 0.0000 + x = 0.513002193 + -0.3725 x = 0.513002193 + -0.3725 Combine like terms: 0.513002193 + -0.3725 = 0.140502193 x = 0.140502193 Simplifying x = 0.140502193Subproblem 2
x + 0.3725 = -0.513002193 Simplifying x + 0.3725 = -0.513002193 Reorder the terms: 0.3725 + x = -0.513002193 Solving 0.3725 + x = -0.513002193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3725' to each side of the equation. 0.3725 + -0.3725 + x = -0.513002193 + -0.3725 Combine like terms: 0.3725 + -0.3725 = 0.0000 0.0000 + x = -0.513002193 + -0.3725 x = -0.513002193 + -0.3725 Combine like terms: -0.513002193 + -0.3725 = -0.885502193 x = -0.885502193 Simplifying x = -0.885502193Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.140502193, -0.885502193}
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