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Simplifying 6x2 + 3x + 8x = 9 + -11x + 3x2 Reorder the terms: 3x + 8x + 6x2 = 9 + -11x + 3x2 Combine like terms: 3x + 8x = 11x 11x + 6x2 = 9 + -11x + 3x2 Solving 11x + 6x2 = 9 + -11x + 3x2 Solving for variable 'x'. Reorder the terms: -9 + 11x + 11x + 6x2 + -3x2 = 9 + -11x + 3x2 + -9 + 11x + -3x2 Combine like terms: 11x + 11x = 22x -9 + 22x + 6x2 + -3x2 = 9 + -11x + 3x2 + -9 + 11x + -3x2 Combine like terms: 6x2 + -3x2 = 3x2 -9 + 22x + 3x2 = 9 + -11x + 3x2 + -9 + 11x + -3x2 Reorder the terms: -9 + 22x + 3x2 = 9 + -9 + -11x + 11x + 3x2 + -3x2 Combine like terms: 9 + -9 = 0 -9 + 22x + 3x2 = 0 + -11x + 11x + 3x2 + -3x2 -9 + 22x + 3x2 = -11x + 11x + 3x2 + -3x2 Combine like terms: -11x + 11x = 0 -9 + 22x + 3x2 = 0 + 3x2 + -3x2 -9 + 22x + 3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -9 + 22x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 7.333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 7.333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 7.333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 7.333333333x + x2 = 0 + 3 7.333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 7.333333333x + x2 = 3 The x term is 7.333333333x. Take half its coefficient (3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. 7.333333333x + 13.44444445 + x2 = 3 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333x + x2 = 3 + 13.44444445 Combine like terms: 3 + 13.44444445 = 16.44444445 13.44444445 + 7.333333333x + x2 = 16.44444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 16.44444445 Calculate the square root of the right side: 4.055175021 Break this problem into two subproblems by setting (x + 3.666666667) equal to 4.055175021 and -4.055175021.Subproblem 1
x + 3.666666667 = 4.055175021 Simplifying x + 3.666666667 = 4.055175021 Reorder the terms: 3.666666667 + x = 4.055175021 Solving 3.666666667 + x = 4.055175021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = 4.055175021 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 4.055175021 + -3.666666667 x = 4.055175021 + -3.666666667 Combine like terms: 4.055175021 + -3.666666667 = 0.388508354 x = 0.388508354 Simplifying x = 0.388508354Subproblem 2
x + 3.666666667 = -4.055175021 Simplifying x + 3.666666667 = -4.055175021 Reorder the terms: 3.666666667 + x = -4.055175021 Solving 3.666666667 + x = -4.055175021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = -4.055175021 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -4.055175021 + -3.666666667 x = -4.055175021 + -3.666666667 Combine like terms: -4.055175021 + -3.666666667 = -7.721841688 x = -7.721841688 Simplifying x = -7.721841688Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.388508354, -7.721841688}
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