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Simplifying 3x2 + -60x + 298 = 0 Reorder the terms: 298 + -60x + 3x2 = 0 Solving 298 + -60x + 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'. 99.33333333 + -20x + x2 = 0 Move the constant term to the right: Add '-99.33333333' to each side of the equation. 99.33333333 + -20x + -99.33333333 + x2 = 0 + -99.33333333 Reorder the terms: 99.33333333 + -99.33333333 + -20x + x2 = 0 + -99.33333333 Combine like terms: 99.33333333 + -99.33333333 = 0.00000000 0.00000000 + -20x + x2 = 0 + -99.33333333 -20x + x2 = 0 + -99.33333333 Combine like terms: 0 + -99.33333333 = -99.33333333 -20x + x2 = -99.33333333 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -99.33333333 + 100 Reorder the terms: 100 + -20x + x2 = -99.33333333 + 100 Combine like terms: -99.33333333 + 100 = 0.66666667 100 + -20x + x2 = 0.66666667 Factor a perfect square on the left side: (x + -10)(x + -10) = 0.66666667 Calculate the square root of the right side: 0.816496583 Break this problem into two subproblems by setting (x + -10) equal to 0.816496583 and -0.816496583.Subproblem 1
x + -10 = 0.816496583 Simplifying x + -10 = 0.816496583 Reorder the terms: -10 + x = 0.816496583 Solving -10 + x = 0.816496583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0.816496583 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0.816496583 + 10 x = 0.816496583 + 10 Combine like terms: 0.816496583 + 10 = 10.816496583 x = 10.816496583 Simplifying x = 10.816496583Subproblem 2
x + -10 = -0.816496583 Simplifying x + -10 = -0.816496583 Reorder the terms: -10 + x = -0.816496583 Solving -10 + x = -0.816496583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -0.816496583 + 10 Combine like terms: -10 + 10 = 0 0 + x = -0.816496583 + 10 x = -0.816496583 + 10 Combine like terms: -0.816496583 + 10 = 9.183503417 x = 9.183503417 Simplifying x = 9.183503417Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.816496583, 9.183503417}
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