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Simplifying 10 + 600x + -3x2 = 0 Solving 10 + 600x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.333333333 + -200x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -200x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -200x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -200x + x2 = 0 + 3.333333333 -200x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -200x + x2 = 3.333333333 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 = 3.333333333 + 10000 Reorder the terms: 10000 + -200x + x2 = 3.333333333 + 10000 Combine like terms: 3.333333333 + 10000 = 10003.333333333 10000 + -200x + x2 = 10003.333333333 Factor a perfect square on the left side: (x + -100)(x + -100) = 10003.333333333 Calculate the square root of the right side: 100.016665278 Break this problem into two subproblems by setting (x + -100) equal to 100.016665278 and -100.016665278.Subproblem 1
x + -100 = 100.016665278 Simplifying x + -100 = 100.016665278 Reorder the terms: -100 + x = 100.016665278 Solving -100 + x = 100.016665278 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 = 100.016665278 + 100 Combine like terms: -100 + 100 = 0 0 + x = 100.016665278 + 100 x = 100.016665278 + 100 Combine like terms: 100.016665278 + 100 = 200.016665278 x = 200.016665278 Simplifying x = 200.016665278Subproblem 2
x + -100 = -100.016665278 Simplifying x + -100 = -100.016665278 Reorder the terms: -100 + x = -100.016665278 Solving -100 + x = -100.016665278 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 = -100.016665278 + 100 Combine like terms: -100 + 100 = 0 0 + x = -100.016665278 + 100 x = -100.016665278 + 100 Combine like terms: -100.016665278 + 100 = -0.016665278 x = -0.016665278 Simplifying x = -0.016665278Solution
The solution to the problem is based on the solutions from the subproblems. x = {200.016665278, -0.016665278}
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