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Simplifying 4x2 + -1200x + -1 = 0 Reorder the terms: -1 + -1200x + 4x2 = 0 Solving -1 + -1200x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -300x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -300x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -300x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -300x + x2 = 0 + 0.25 -300x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -300x + x2 = 0.25 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = 0.25 + 22500 Reorder the terms: 22500 + -300x + x2 = 0.25 + 22500 Combine like terms: 0.25 + 22500 = 22500.25 22500 + -300x + x2 = 22500.25 Factor a perfect square on the left side: (x + -150)(x + -150) = 22500.25 Calculate the square root of the right side: 150.000833331 Break this problem into two subproblems by setting (x + -150) equal to 150.000833331 and -150.000833331.Subproblem 1
x + -150 = 150.000833331 Simplifying x + -150 = 150.000833331 Reorder the terms: -150 + x = 150.000833331 Solving -150 + x = 150.000833331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 150.000833331 + 150 Combine like terms: -150 + 150 = 0 0 + x = 150.000833331 + 150 x = 150.000833331 + 150 Combine like terms: 150.000833331 + 150 = 300.000833331 x = 300.000833331 Simplifying x = 300.000833331Subproblem 2
x + -150 = -150.000833331 Simplifying x + -150 = -150.000833331 Reorder the terms: -150 + x = -150.000833331 Solving -150 + x = -150.000833331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -150.000833331 + 150 Combine like terms: -150 + 150 = 0 0 + x = -150.000833331 + 150 x = -150.000833331 + 150 Combine like terms: -150.000833331 + 150 = -0.000833331 x = -0.000833331 Simplifying x = -0.000833331Solution
The solution to the problem is based on the solutions from the subproblems. x = {300.000833331, -0.000833331}
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