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Simplifying -1x2 + 300x + 10000 = 0 Reorder the terms: 10000 + 300x + -1x2 = 0 Solving 10000 + 300x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10000 + -300x + x2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + -300x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + -300x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + -300x + x2 = 0 + 10000 -300x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 -300x + x2 = 10000 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 = 10000 + 22500 Reorder the terms: 22500 + -300x + x2 = 10000 + 22500 Combine like terms: 10000 + 22500 = 32500 22500 + -300x + x2 = 32500 Factor a perfect square on the left side: (x + -150)(x + -150) = 32500 Calculate the square root of the right side: 180.277563773 Break this problem into two subproblems by setting (x + -150) equal to 180.277563773 and -180.277563773.Subproblem 1
x + -150 = 180.277563773 Simplifying x + -150 = 180.277563773 Reorder the terms: -150 + x = 180.277563773 Solving -150 + x = 180.277563773 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 = 180.277563773 + 150 Combine like terms: -150 + 150 = 0 0 + x = 180.277563773 + 150 x = 180.277563773 + 150 Combine like terms: 180.277563773 + 150 = 330.277563773 x = 330.277563773 Simplifying x = 330.277563773Subproblem 2
x + -150 = -180.277563773 Simplifying x + -150 = -180.277563773 Reorder the terms: -150 + x = -180.277563773 Solving -150 + x = -180.277563773 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 = -180.277563773 + 150 Combine like terms: -150 + 150 = 0 0 + x = -180.277563773 + 150 x = -180.277563773 + 150 Combine like terms: -180.277563773 + 150 = -30.277563773 x = -30.277563773 Simplifying x = -30.277563773Solution
The solution to the problem is based on the solutions from the subproblems. x = {330.277563773, -30.277563773}
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