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Simplifying -3x2 + 228x + -1000 = 18 Reorder the terms: -1000 + 228x + -3x2 = 18 Solving -1000 + 228x + -3x2 = 18 Solving for variable 'x'. Reorder the terms: -1000 + -18 + 228x + -3x2 = 18 + -18 Combine like terms: -1000 + -18 = -1018 -1018 + 228x + -3x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -1018 + 228x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 339.3333333 + -76x + x2 = 0 Move the constant term to the right: Add '-339.3333333' to each side of the equation. 339.3333333 + -76x + -339.3333333 + x2 = 0 + -339.3333333 Reorder the terms: 339.3333333 + -339.3333333 + -76x + x2 = 0 + -339.3333333 Combine like terms: 339.3333333 + -339.3333333 = 0.0000000 0.0000000 + -76x + x2 = 0 + -339.3333333 -76x + x2 = 0 + -339.3333333 Combine like terms: 0 + -339.3333333 = -339.3333333 -76x + x2 = -339.3333333 The x term is -76x. Take half its coefficient (-38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. -76x + 1444 + x2 = -339.3333333 + 1444 Reorder the terms: 1444 + -76x + x2 = -339.3333333 + 1444 Combine like terms: -339.3333333 + 1444 = 1104.6666667 1444 + -76x + x2 = 1104.6666667 Factor a perfect square on the left side: (x + -38)(x + -38) = 1104.6666667 Calculate the square root of the right side: 33.236526093 Break this problem into two subproblems by setting (x + -38) equal to 33.236526093 and -33.236526093.Subproblem 1
x + -38 = 33.236526093 Simplifying x + -38 = 33.236526093 Reorder the terms: -38 + x = 33.236526093 Solving -38 + x = 33.236526093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + x = 33.236526093 + 38 Combine like terms: -38 + 38 = 0 0 + x = 33.236526093 + 38 x = 33.236526093 + 38 Combine like terms: 33.236526093 + 38 = 71.236526093 x = 71.236526093 Simplifying x = 71.236526093Subproblem 2
x + -38 = -33.236526093 Simplifying x + -38 = -33.236526093 Reorder the terms: -38 + x = -33.236526093 Solving -38 + x = -33.236526093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + x = -33.236526093 + 38 Combine like terms: -38 + 38 = 0 0 + x = -33.236526093 + 38 x = -33.236526093 + 38 Combine like terms: -33.236526093 + 38 = 4.763473907 x = 4.763473907 Simplifying x = 4.763473907Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.236526093, 4.763473907}
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