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Simplifying -1x2 + 100x + -300 = 0 Reorder the terms: -300 + 100x + -1x2 = 0 Solving -300 + 100x + -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'. 300 + -100x + x2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -100x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -100x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -100x + x2 = 0 + -300 -100x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -100x + x2 = -300 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -300 + 2500 Reorder the terms: 2500 + -100x + x2 = -300 + 2500 Combine like terms: -300 + 2500 = 2200 2500 + -100x + x2 = 2200 Factor a perfect square on the left side: (x + -50)(x + -50) = 2200 Calculate the square root of the right side: 46.904157598 Break this problem into two subproblems by setting (x + -50) equal to 46.904157598 and -46.904157598.Subproblem 1
x + -50 = 46.904157598 Simplifying x + -50 = 46.904157598 Reorder the terms: -50 + x = 46.904157598 Solving -50 + x = 46.904157598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 46.904157598 + 50 Combine like terms: -50 + 50 = 0 0 + x = 46.904157598 + 50 x = 46.904157598 + 50 Combine like terms: 46.904157598 + 50 = 96.904157598 x = 96.904157598 Simplifying x = 96.904157598Subproblem 2
x + -50 = -46.904157598 Simplifying x + -50 = -46.904157598 Reorder the terms: -50 + x = -46.904157598 Solving -50 + x = -46.904157598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -46.904157598 + 50 Combine like terms: -50 + 50 = 0 0 + x = -46.904157598 + 50 x = -46.904157598 + 50 Combine like terms: -46.904157598 + 50 = 3.095842402 x = 3.095842402 Simplifying x = 3.095842402Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.904157598, 3.095842402}
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