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Simplifying x2 + -83x = 1500 Reorder the terms: -83x + x2 = 1500 Solving -83x + x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + -83x + x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + -83x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1500' to each side of the equation. -1500 + -83x + 1500 + x2 = 0 + 1500 Reorder the terms: -1500 + 1500 + -83x + x2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + -83x + x2 = 0 + 1500 -83x + x2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 -83x + x2 = 1500 The x term is -83x. Take half its coefficient (-41.5). Square it (1722.25) and add it to both sides. Add '1722.25' to each side of the equation. -83x + 1722.25 + x2 = 1500 + 1722.25 Reorder the terms: 1722.25 + -83x + x2 = 1500 + 1722.25 Combine like terms: 1500 + 1722.25 = 3222.25 1722.25 + -83x + x2 = 3222.25 Factor a perfect square on the left side: (x + -41.5)(x + -41.5) = 3222.25 Calculate the square root of the right side: 56.764865894 Break this problem into two subproblems by setting (x + -41.5) equal to 56.764865894 and -56.764865894.Subproblem 1
x + -41.5 = 56.764865894 Simplifying x + -41.5 = 56.764865894 Reorder the terms: -41.5 + x = 56.764865894 Solving -41.5 + x = 56.764865894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41.5' to each side of the equation. -41.5 + 41.5 + x = 56.764865894 + 41.5 Combine like terms: -41.5 + 41.5 = 0.0 0.0 + x = 56.764865894 + 41.5 x = 56.764865894 + 41.5 Combine like terms: 56.764865894 + 41.5 = 98.264865894 x = 98.264865894 Simplifying x = 98.264865894Subproblem 2
x + -41.5 = -56.764865894 Simplifying x + -41.5 = -56.764865894 Reorder the terms: -41.5 + x = -56.764865894 Solving -41.5 + x = -56.764865894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41.5' to each side of the equation. -41.5 + 41.5 + x = -56.764865894 + 41.5 Combine like terms: -41.5 + 41.5 = 0.0 0.0 + x = -56.764865894 + 41.5 x = -56.764865894 + 41.5 Combine like terms: -56.764865894 + 41.5 = -15.264865894 x = -15.264865894 Simplifying x = -15.264865894Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.264865894, -15.264865894}
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