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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 = 1234125 1265625 + -2250x + x2 = 1234125 Factor a perfect square on the left side: (x + -1125)(x + -1125) = 1234125 Calculate the square root of the right side: 1110.911787677 Break this problem into two subproblems by setting (x + -1125) equal to 1110.911787677 and -1110.911787677.Subproblem 1
x + -1125 = 1110.911787677 Simplifying x + -1125 = 1110.911787677 Reorder the terms: -1125 + x = 1110.911787677 Solving -1125 + x = 1110.911787677 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 = 1110.911787677 + 1125 Combine like terms: -1125 + 1125 = 0 0 + x = 1110.911787677 + 1125 x = 1110.911787677 + 1125 Combine like terms: 1110.911787677 + 1125 = 2235.911787677 x = 2235.911787677 Simplifying x = 2235.911787677Subproblem 2
x + -1125 = -1110.911787677 Simplifying x + -1125 = -1110.911787677 Reorder the terms: -1125 + x = -1110.911787677 Solving -1125 + x = -1110.911787677 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 = -1110.911787677 + 1125 Combine like terms: -1125 + 1125 = 0 0 + x = -1110.911787677 + 1125 x = -1110.911787677 + 1125 Combine like terms: -1110.911787677 + 1125 = 14.088212323 x = 14.088212323 Simplifying x = 14.088212323Solution
The solution to the problem is based on the solutions from the subproblems. x = {2235.911787677, 14.088212323}
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