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Simplifying -0.006x2 + 1.2x + 1 = 0 Reorder the terms: 1 + 1.2x + -0.006x2 = 0 Solving 1 + 1.2x + -0.006x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.006 the coefficient of the squared term: Divide each side by '-0.006'. -166.6666667 + -200x + x2 = 0 Move the constant term to the right: Add '166.6666667' to each side of the equation. -166.6666667 + -200x + 166.6666667 + x2 = 0 + 166.6666667 Reorder the terms: -166.6666667 + 166.6666667 + -200x + x2 = 0 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + -200x + x2 = 0 + 166.6666667 -200x + x2 = 0 + 166.6666667 Combine like terms: 0 + 166.6666667 = 166.6666667 -200x + x2 = 166.6666667 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 = 166.6666667 + 10000 Reorder the terms: 10000 + -200x + x2 = 166.6666667 + 10000 Combine like terms: 166.6666667 + 10000 = 10166.6666667 10000 + -200x + x2 = 10166.6666667 Factor a perfect square on the left side: (x + -100)(x + -100) = 10166.6666667 Calculate the square root of the right side: 100.829889749 Break this problem into two subproblems by setting (x + -100) equal to 100.829889749 and -100.829889749.Subproblem 1
x + -100 = 100.829889749 Simplifying x + -100 = 100.829889749 Reorder the terms: -100 + x = 100.829889749 Solving -100 + x = 100.829889749 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 = 100.829889749 + 100 Combine like terms: -100 + 100 = 0 0 + x = 100.829889749 + 100 x = 100.829889749 + 100 Combine like terms: 100.829889749 + 100 = 200.829889749 x = 200.829889749 Simplifying x = 200.829889749Subproblem 2
x + -100 = -100.829889749 Simplifying x + -100 = -100.829889749 Reorder the terms: -100 + x = -100.829889749 Solving -100 + x = -100.829889749 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 = -100.829889749 + 100 Combine like terms: -100 + 100 = 0 0 + x = -100.829889749 + 100 x = -100.829889749 + 100 Combine like terms: -100.829889749 + 100 = -0.829889749 x = -0.829889749 Simplifying x = -0.829889749Solution
The solution to the problem is based on the solutions from the subproblems. x = {200.829889749, -0.829889749}
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