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Simplifying 0.14x + -1(1.8 + 0.12x + -0.0001x2) = 0 0.14x + (1.8 * -1 + 0.12x * -1 + -0.0001x2 * -1) = 0 0.14x + (-1.8 + -0.12x + 0.0001x2) = 0 Reorder the terms: -1.8 + 0.14x + -0.12x + 0.0001x2 = 0 Combine like terms: 0.14x + -0.12x = 0.02x -1.8 + 0.02x + 0.0001x2 = 0 Solving -1.8 + 0.02x + 0.0001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. -18000 + 200x + x2 = 0 Move the constant term to the right: Add '18000' to each side of the equation. -18000 + 200x + 18000 + x2 = 0 + 18000 Reorder the terms: -18000 + 18000 + 200x + x2 = 0 + 18000 Combine like terms: -18000 + 18000 = 0 0 + 200x + x2 = 0 + 18000 200x + x2 = 0 + 18000 Combine like terms: 0 + 18000 = 18000 200x + x2 = 18000 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = 18000 + 10000 Reorder the terms: 10000 + 200x + x2 = 18000 + 10000 Combine like terms: 18000 + 10000 = 28000 10000 + 200x + x2 = 28000 Factor a perfect square on the left side: (x + 100)(x + 100) = 28000 Calculate the square root of the right side: 167.332005307 Break this problem into two subproblems by setting (x + 100) equal to 167.332005307 and -167.332005307.Subproblem 1
x + 100 = 167.332005307 Simplifying x + 100 = 167.332005307 Reorder the terms: 100 + x = 167.332005307 Solving 100 + x = 167.332005307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 167.332005307 + -100 Combine like terms: 100 + -100 = 0 0 + x = 167.332005307 + -100 x = 167.332005307 + -100 Combine like terms: 167.332005307 + -100 = 67.332005307 x = 67.332005307 Simplifying x = 67.332005307Subproblem 2
x + 100 = -167.332005307 Simplifying x + 100 = -167.332005307 Reorder the terms: 100 + x = -167.332005307 Solving 100 + x = -167.332005307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -167.332005307 + -100 Combine like terms: 100 + -100 = 0 0 + x = -167.332005307 + -100 x = -167.332005307 + -100 Combine like terms: -167.332005307 + -100 = -267.332005307 x = -267.332005307 Simplifying x = -267.332005307Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.332005307, -267.332005307}
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