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Simplifying 6x2 + -47x + -75 = 0 Reorder the terms: -75 + -47x + 6x2 = 0 Solving -75 + -47x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -12.5 + -7.833333333x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -7.833333333x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -7.833333333x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -7.833333333x + x2 = 0 + 12.5 -7.833333333x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -7.833333333x + x2 = 12.5 The x term is -7.833333333x. Take half its coefficient (-3.916666667). Square it (15.34027778) and add it to both sides. Add '15.34027778' to each side of the equation. -7.833333333x + 15.34027778 + x2 = 12.5 + 15.34027778 Reorder the terms: 15.34027778 + -7.833333333x + x2 = 12.5 + 15.34027778 Combine like terms: 12.5 + 15.34027778 = 27.84027778 15.34027778 + -7.833333333x + x2 = 27.84027778 Factor a perfect square on the left side: (x + -3.916666667)(x + -3.916666667) = 27.84027778 Calculate the square root of the right side: 5.276388706 Break this problem into two subproblems by setting (x + -3.916666667) equal to 5.276388706 and -5.276388706.Subproblem 1
x + -3.916666667 = 5.276388706 Simplifying x + -3.916666667 = 5.276388706 Reorder the terms: -3.916666667 + x = 5.276388706 Solving -3.916666667 + x = 5.276388706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.916666667' to each side of the equation. -3.916666667 + 3.916666667 + x = 5.276388706 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + x = 5.276388706 + 3.916666667 x = 5.276388706 + 3.916666667 Combine like terms: 5.276388706 + 3.916666667 = 9.193055373 x = 9.193055373 Simplifying x = 9.193055373Subproblem 2
x + -3.916666667 = -5.276388706 Simplifying x + -3.916666667 = -5.276388706 Reorder the terms: -3.916666667 + x = -5.276388706 Solving -3.916666667 + x = -5.276388706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.916666667' to each side of the equation. -3.916666667 + 3.916666667 + x = -5.276388706 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + x = -5.276388706 + 3.916666667 x = -5.276388706 + 3.916666667 Combine like terms: -5.276388706 + 3.916666667 = -1.359722039 x = -1.359722039 Simplifying x = -1.359722039Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.193055373, -1.359722039}
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