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Simplifying -1x2 + 300x = 50 Reorder the terms: 300x + -1x2 = 50 Solving 300x + -1x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 300x + -1x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 300x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -300x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -300x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -300x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -300x + x2 = 0 + -50 -300x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -300x + x2 = -50 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 = -50 + 22500 Reorder the terms: 22500 + -300x + x2 = -50 + 22500 Combine like terms: -50 + 22500 = 22450 22500 + -300x + x2 = 22450 Factor a perfect square on the left side: (x + -150)(x + -150) = 22450 Calculate the square root of the right side: 149.833240638 Break this problem into two subproblems by setting (x + -150) equal to 149.833240638 and -149.833240638.Subproblem 1
x + -150 = 149.833240638 Simplifying x + -150 = 149.833240638 Reorder the terms: -150 + x = 149.833240638 Solving -150 + x = 149.833240638 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 = 149.833240638 + 150 Combine like terms: -150 + 150 = 0 0 + x = 149.833240638 + 150 x = 149.833240638 + 150 Combine like terms: 149.833240638 + 150 = 299.833240638 x = 299.833240638 Simplifying x = 299.833240638Subproblem 2
x + -150 = -149.833240638 Simplifying x + -150 = -149.833240638 Reorder the terms: -150 + x = -149.833240638 Solving -150 + x = -149.833240638 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 = -149.833240638 + 150 Combine like terms: -150 + 150 = 0 0 + x = -149.833240638 + 150 x = -149.833240638 + 150 Combine like terms: -149.833240638 + 150 = 0.166759362 x = 0.166759362 Simplifying x = 0.166759362Solution
The solution to the problem is based on the solutions from the subproblems. x = {299.833240638, 0.166759362}
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