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Simplifying x2 + -2250x + -31500 = 0 Reorder the terms: -31500 + -2250x + x2 = 0 Solving -31500 + -2250x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '31500' to each side of the equation. -31500 + -2250x + 31500 + x2 = 0 + 31500 Reorder the terms: -31500 + 31500 + -2250x + x2 = 0 + 31500 Combine like terms: -31500 + 31500 = 0 0 + -2250x + x2 = 0 + 31500 -2250x + x2 = 0 + 31500 Combine like terms: 0 + 31500 = 31500 -2250x + x2 = 31500 The x term is -2250x. Take half its coefficient (-1125). Square it (1265625) and add it to both sides. Add '1265625' to each side of the equation. -2250x + 1265625 + x2 = 31500 + 1265625 Reorder the terms: 1265625 + -2250x + x2 = 31500 + 1265625 Combine like terms: 31500 + 1265625 = 1297125 1265625 + -2250x + x2 = 1297125 Factor a perfect square on the left side: (x + -1125)(x + -1125) = 1297125 Calculate the square root of the right side: 1138.913956364 Break this problem into two subproblems by setting (x + -1125) equal to 1138.913956364 and -1138.913956364.Subproblem 1
x + -1125 = 1138.913956364 Simplifying x + -1125 = 1138.913956364 Reorder the terms: -1125 + x = 1138.913956364 Solving -1125 + x = 1138.913956364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1125' to each side of the equation. -1125 + 1125 + x = 1138.913956364 + 1125 Combine like terms: -1125 + 1125 = 0 0 + x = 1138.913956364 + 1125 x = 1138.913956364 + 1125 Combine like terms: 1138.913956364 + 1125 = 2263.913956364 x = 2263.913956364 Simplifying x = 2263.913956364Subproblem 2
x + -1125 = -1138.913956364 Simplifying x + -1125 = -1138.913956364 Reorder the terms: -1125 + x = -1138.913956364 Solving -1125 + x = -1138.913956364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1125' to each side of the equation. -1125 + 1125 + x = -1138.913956364 + 1125 Combine like terms: -1125 + 1125 = 0 0 + x = -1138.913956364 + 1125 x = -1138.913956364 + 1125 Combine like terms: -1138.913956364 + 1125 = -13.913956364 x = -13.913956364 Simplifying x = -13.913956364Solution
The solution to the problem is based on the solutions from the subproblems. x = {2263.913956364, -13.913956364}
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