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Simplifying 6x2 + -47x + 128 = 216 Reorder the terms: 128 + -47x + 6x2 = 216 Solving 128 + -47x + 6x2 = 216 Solving for variable 'x'. Reorder the terms: 128 + -216 + -47x + 6x2 = 216 + -216 Combine like terms: 128 + -216 = -88 -88 + -47x + 6x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -88 + -47x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -14.66666667 + -7.833333333x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + -7.833333333x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + -7.833333333x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + -7.833333333x + x2 = 0 + 14.66666667 -7.833333333x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 -7.833333333x + x2 = 14.66666667 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 = 14.66666667 + 15.34027778 Reorder the terms: 15.34027778 + -7.833333333x + x2 = 14.66666667 + 15.34027778 Combine like terms: 14.66666667 + 15.34027778 = 30.00694445 15.34027778 + -7.833333333x + x2 = 30.00694445 Factor a perfect square on the left side: (x + -3.916666667)(x + -3.916666667) = 30.00694445 Calculate the square root of the right side: 5.477859477 Break this problem into two subproblems by setting (x + -3.916666667) equal to 5.477859477 and -5.477859477.Subproblem 1
x + -3.916666667 = 5.477859477 Simplifying x + -3.916666667 = 5.477859477 Reorder the terms: -3.916666667 + x = 5.477859477 Solving -3.916666667 + x = 5.477859477 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 = 5.477859477 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + x = 5.477859477 + 3.916666667 x = 5.477859477 + 3.916666667 Combine like terms: 5.477859477 + 3.916666667 = 9.394526144 x = 9.394526144 Simplifying x = 9.394526144Subproblem 2
x + -3.916666667 = -5.477859477 Simplifying x + -3.916666667 = -5.477859477 Reorder the terms: -3.916666667 + x = -5.477859477 Solving -3.916666667 + x = -5.477859477 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 = -5.477859477 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + x = -5.477859477 + 3.916666667 x = -5.477859477 + 3.916666667 Combine like terms: -5.477859477 + 3.916666667 = -1.56119281 x = -1.56119281 Simplifying x = -1.56119281Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.394526144, -1.56119281}
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