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Simplifying 3x2 + -7000x + 1750000 = 0 Reorder the terms: 1750000 + -7000x + 3x2 = 0 Solving 1750000 + -7000x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 583333.3333 + -2333.333333x + x2 = 0 Move the constant term to the right: Add '-583333.3333' to each side of the equation. 583333.3333 + -2333.333333x + -583333.3333 + x2 = 0 + -583333.3333 Reorder the terms: 583333.3333 + -583333.3333 + -2333.333333x + x2 = 0 + -583333.3333 Combine like terms: 583333.3333 + -583333.3333 = 0.0000 0.0000 + -2333.333333x + x2 = 0 + -583333.3333 -2333.333333x + x2 = 0 + -583333.3333 Combine like terms: 0 + -583333.3333 = -583333.3333 -2333.333333x + x2 = -583333.3333 The x term is -2333.333333x. Take half its coefficient (-1166.666667). Square it (1361111.112) and add it to both sides. Add '1361111.112' to each side of the equation. -2333.333333x + 1361111.112 + x2 = -583333.3333 + 1361111.112 Reorder the terms: 1361111.112 + -2333.333333x + x2 = -583333.3333 + 1361111.112 Combine like terms: -583333.3333 + 1361111.112 = 777777.7787 1361111.112 + -2333.333333x + x2 = 777777.7787 Factor a perfect square on the left side: (x + -1166.666667)(x + -1166.666667) = 777777.7787 Calculate the square root of the right side: 881.917104211 Break this problem into two subproblems by setting (x + -1166.666667) equal to 881.917104211 and -881.917104211.Subproblem 1
x + -1166.666667 = 881.917104211 Simplifying x + -1166.666667 = 881.917104211 Reorder the terms: -1166.666667 + x = 881.917104211 Solving -1166.666667 + x = 881.917104211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1166.666667' to each side of the equation. -1166.666667 + 1166.666667 + x = 881.917104211 + 1166.666667 Combine like terms: -1166.666667 + 1166.666667 = 0.000000 0.000000 + x = 881.917104211 + 1166.666667 x = 881.917104211 + 1166.666667 Combine like terms: 881.917104211 + 1166.666667 = 2048.583771211 x = 2048.583771211 Simplifying x = 2048.583771211Subproblem 2
x + -1166.666667 = -881.917104211 Simplifying x + -1166.666667 = -881.917104211 Reorder the terms: -1166.666667 + x = -881.917104211 Solving -1166.666667 + x = -881.917104211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1166.666667' to each side of the equation. -1166.666667 + 1166.666667 + x = -881.917104211 + 1166.666667 Combine like terms: -1166.666667 + 1166.666667 = 0.000000 0.000000 + x = -881.917104211 + 1166.666667 x = -881.917104211 + 1166.666667 Combine like terms: -881.917104211 + 1166.666667 = 284.749562789 x = 284.749562789 Simplifying x = 284.749562789Solution
The solution to the problem is based on the solutions from the subproblems. x = {2048.583771211, 284.749562789}
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