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Simplifying x2 + -2x + -7500 = 0 Reorder the terms: -7500 + -2x + x2 = 0 Solving -7500 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7500' to each side of the equation. -7500 + -2x + 7500 + x2 = 0 + 7500 Reorder the terms: -7500 + 7500 + -2x + x2 = 0 + 7500 Combine like terms: -7500 + 7500 = 0 0 + -2x + x2 = 0 + 7500 -2x + x2 = 0 + 7500 Combine like terms: 0 + 7500 = 7500 -2x + x2 = 7500 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 7500 + 1 Reorder the terms: 1 + -2x + x2 = 7500 + 1 Combine like terms: 7500 + 1 = 7501 1 + -2x + x2 = 7501 Factor a perfect square on the left side: (x + -1)(x + -1) = 7501 Calculate the square root of the right side: 86.608313689 Break this problem into two subproblems by setting (x + -1) equal to 86.608313689 and -86.608313689.Subproblem 1
x + -1 = 86.608313689 Simplifying x + -1 = 86.608313689 Reorder the terms: -1 + x = 86.608313689 Solving -1 + x = 86.608313689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 86.608313689 + 1 Combine like terms: -1 + 1 = 0 0 + x = 86.608313689 + 1 x = 86.608313689 + 1 Combine like terms: 86.608313689 + 1 = 87.608313689 x = 87.608313689 Simplifying x = 87.608313689Subproblem 2
x + -1 = -86.608313689 Simplifying x + -1 = -86.608313689 Reorder the terms: -1 + x = -86.608313689 Solving -1 + x = -86.608313689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -86.608313689 + 1 Combine like terms: -1 + 1 = 0 0 + x = -86.608313689 + 1 x = -86.608313689 + 1 Combine like terms: -86.608313689 + 1 = -85.608313689 x = -85.608313689 Simplifying x = -85.608313689Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.608313689, -85.608313689}
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