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Simplifying x2 + -100x + -300 = 0 Reorder the terms: -300 + -100x + x2 = 0 Solving -300 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. 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 = 2800 2500 + -100x + x2 = 2800 Factor a perfect square on the left side: (x + -50)(x + -50) = 2800 Calculate the square root of the right side: 52.915026221 Break this problem into two subproblems by setting (x + -50) equal to 52.915026221 and -52.915026221.Subproblem 1
x + -50 = 52.915026221 Simplifying x + -50 = 52.915026221 Reorder the terms: -50 + x = 52.915026221 Solving -50 + x = 52.915026221 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 = 52.915026221 + 50 Combine like terms: -50 + 50 = 0 0 + x = 52.915026221 + 50 x = 52.915026221 + 50 Combine like terms: 52.915026221 + 50 = 102.915026221 x = 102.915026221 Simplifying x = 102.915026221Subproblem 2
x + -50 = -52.915026221 Simplifying x + -50 = -52.915026221 Reorder the terms: -50 + x = -52.915026221 Solving -50 + x = -52.915026221 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 = -52.915026221 + 50 Combine like terms: -50 + 50 = 0 0 + x = -52.915026221 + 50 x = -52.915026221 + 50 Combine like terms: -52.915026221 + 50 = -2.915026221 x = -2.915026221 Simplifying x = -2.915026221Solution
The solution to the problem is based on the solutions from the subproblems. x = {102.915026221, -2.915026221}
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