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Simplifying 150 = x2 + -300x Reorder the terms: 150 = -300x + x2 Solving 150 = -300x + x2 Solving for variable 'x'. Reorder the terms: 150 + 300x + -1x2 = -300x + 300x + x2 + -1x2 Combine like terms: -300x + 300x = 0 150 + 300x + -1x2 = 0 + x2 + -1x2 150 + 300x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 150 + 300x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -150 + -300x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + -300x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -300x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -300x + x2 = 0 + 150 -300x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -300x + x2 = 150 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 = 150 + 22500 Reorder the terms: 22500 + -300x + x2 = 150 + 22500 Combine like terms: 150 + 22500 = 22650 22500 + -300x + x2 = 22650 Factor a perfect square on the left side: (x + -150)(x + -150) = 22650 Calculate the square root of the right side: 150.499169433 Break this problem into two subproblems by setting (x + -150) equal to 150.499169433 and -150.499169433.Subproblem 1
x + -150 = 150.499169433 Simplifying x + -150 = 150.499169433 Reorder the terms: -150 + x = 150.499169433 Solving -150 + x = 150.499169433 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 = 150.499169433 + 150 Combine like terms: -150 + 150 = 0 0 + x = 150.499169433 + 150 x = 150.499169433 + 150 Combine like terms: 150.499169433 + 150 = 300.499169433 x = 300.499169433 Simplifying x = 300.499169433Subproblem 2
x + -150 = -150.499169433 Simplifying x + -150 = -150.499169433 Reorder the terms: -150 + x = -150.499169433 Solving -150 + x = -150.499169433 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 = -150.499169433 + 150 Combine like terms: -150 + 150 = 0 0 + x = -150.499169433 + 150 x = -150.499169433 + 150 Combine like terms: -150.499169433 + 150 = -0.499169433 x = -0.499169433 Simplifying x = -0.499169433Solution
The solution to the problem is based on the solutions from the subproblems. x = {300.499169433, -0.499169433}
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