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Simplifying 0.0006x2 + -0.84x + 0.8 = 0 Reorder the terms: 0.8 + -0.84x + 0.0006x2 = 0 Solving 0.8 + -0.84x + 0.0006x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0006 the coefficient of the squared term: Divide each side by '0.0006'. 1333.333333 + -1400x + x2 = 0 Move the constant term to the right: Add '-1333.333333' to each side of the equation. 1333.333333 + -1400x + -1333.333333 + x2 = 0 + -1333.333333 Reorder the terms: 1333.333333 + -1333.333333 + -1400x + x2 = 0 + -1333.333333 Combine like terms: 1333.333333 + -1333.333333 = 0.000000 0.000000 + -1400x + x2 = 0 + -1333.333333 -1400x + x2 = 0 + -1333.333333 Combine like terms: 0 + -1333.333333 = -1333.333333 -1400x + x2 = -1333.333333 The x term is -1400x. Take half its coefficient (-700). Square it (490000) and add it to both sides. Add '490000' to each side of the equation. -1400x + 490000 + x2 = -1333.333333 + 490000 Reorder the terms: 490000 + -1400x + x2 = -1333.333333 + 490000 Combine like terms: -1333.333333 + 490000 = 488666.666667 490000 + -1400x + x2 = 488666.666667 Factor a perfect square on the left side: (x + -700)(x + -700) = 488666.666667 Calculate the square root of the right side: 699.046970287 Break this problem into two subproblems by setting (x + -700) equal to 699.046970287 and -699.046970287.Subproblem 1
x + -700 = 699.046970287 Simplifying x + -700 = 699.046970287 Reorder the terms: -700 + x = 699.046970287 Solving -700 + x = 699.046970287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '700' to each side of the equation. -700 + 700 + x = 699.046970287 + 700 Combine like terms: -700 + 700 = 0 0 + x = 699.046970287 + 700 x = 699.046970287 + 700 Combine like terms: 699.046970287 + 700 = 1399.046970287 x = 1399.046970287 Simplifying x = 1399.046970287Subproblem 2
x + -700 = -699.046970287 Simplifying x + -700 = -699.046970287 Reorder the terms: -700 + x = -699.046970287 Solving -700 + x = -699.046970287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '700' to each side of the equation. -700 + 700 + x = -699.046970287 + 700 Combine like terms: -700 + 700 = 0 0 + x = -699.046970287 + 700 x = -699.046970287 + 700 Combine like terms: -699.046970287 + 700 = 0.953029713 x = 0.953029713 Simplifying x = 0.953029713Solution
The solution to the problem is based on the solutions from the subproblems. x = {1399.046970287, 0.953029713}
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