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Simplifying x2 + -30000 = 100x Reorder the terms: -30000 + x2 = 100x Solving -30000 + x2 = 100x Solving for variable 'x'. Reorder the terms: -30000 + -100x + x2 = 100x + -100x Combine like terms: 100x + -100x = 0 -30000 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30000' to each side of the equation. -30000 + -100x + 30000 + x2 = 0 + 30000 Reorder the terms: -30000 + 30000 + -100x + x2 = 0 + 30000 Combine like terms: -30000 + 30000 = 0 0 + -100x + x2 = 0 + 30000 -100x + x2 = 0 + 30000 Combine like terms: 0 + 30000 = 30000 -100x + x2 = 30000 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 = 30000 + 2500 Reorder the terms: 2500 + -100x + x2 = 30000 + 2500 Combine like terms: 30000 + 2500 = 32500 2500 + -100x + x2 = 32500 Factor a perfect square on the left side: (x + -50)(x + -50) = 32500 Calculate the square root of the right side: 180.277563773 Break this problem into two subproblems by setting (x + -50) equal to 180.277563773 and -180.277563773.Subproblem 1
x + -50 = 180.277563773 Simplifying x + -50 = 180.277563773 Reorder the terms: -50 + x = 180.277563773 Solving -50 + x = 180.277563773 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 = 180.277563773 + 50 Combine like terms: -50 + 50 = 0 0 + x = 180.277563773 + 50 x = 180.277563773 + 50 Combine like terms: 180.277563773 + 50 = 230.277563773 x = 230.277563773 Simplifying x = 230.277563773Subproblem 2
x + -50 = -180.277563773 Simplifying x + -50 = -180.277563773 Reorder the terms: -50 + x = -180.277563773 Solving -50 + x = -180.277563773 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 = -180.277563773 + 50 Combine like terms: -50 + 50 = 0 0 + x = -180.277563773 + 50 x = -180.277563773 + 50 Combine like terms: -180.277563773 + 50 = -130.277563773 x = -130.277563773 Simplifying x = -130.277563773Solution
The solution to the problem is based on the solutions from the subproblems. x = {230.277563773, -130.277563773}
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