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Simplifying 3x2 + -22x = 6x2 + -5x + -8 Reorder the terms: -22x + 3x2 = 6x2 + -5x + -8 Reorder the terms: -22x + 3x2 = -8 + -5x + 6x2 Solving -22x + 3x2 = -8 + -5x + 6x2 Solving for variable 'x'. Reorder the terms: 8 + -22x + 5x + 3x2 + -6x2 = -8 + -5x + 6x2 + 8 + 5x + -6x2 Combine like terms: -22x + 5x = -17x 8 + -17x + 3x2 + -6x2 = -8 + -5x + 6x2 + 8 + 5x + -6x2 Combine like terms: 3x2 + -6x2 = -3x2 8 + -17x + -3x2 = -8 + -5x + 6x2 + 8 + 5x + -6x2 Reorder the terms: 8 + -17x + -3x2 = -8 + 8 + -5x + 5x + 6x2 + -6x2 Combine like terms: -8 + 8 = 0 8 + -17x + -3x2 = 0 + -5x + 5x + 6x2 + -6x2 8 + -17x + -3x2 = -5x + 5x + 6x2 + -6x2 Combine like terms: -5x + 5x = 0 8 + -17x + -3x2 = 0 + 6x2 + -6x2 8 + -17x + -3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 8 + -17x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.666666667 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 5.666666667x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 5.666666667x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 5.666666667x + x2 = 0 + 2.666666667 5.666666667x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 5.666666667x + x2 = 2.666666667 The x term is 5.666666667x. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x + 8.027777782 + x2 = 2.666666667 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 2.666666667 + 8.027777782 Combine like terms: 2.666666667 + 8.027777782 = 10.694444449 8.027777782 + 5.666666667x + x2 = 10.694444449 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 10.694444449 Calculate the square root of the right side: 3.270236146 Break this problem into two subproblems by setting (x + 2.833333334) equal to 3.270236146 and -3.270236146.Subproblem 1
x + 2.833333334 = 3.270236146 Simplifying x + 2.833333334 = 3.270236146 Reorder the terms: 2.833333334 + x = 3.270236146 Solving 2.833333334 + x = 3.270236146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 3.270236146 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 3.270236146 + -2.833333334 x = 3.270236146 + -2.833333334 Combine like terms: 3.270236146 + -2.833333334 = 0.436902812 x = 0.436902812 Simplifying x = 0.436902812Subproblem 2
x + 2.833333334 = -3.270236146 Simplifying x + 2.833333334 = -3.270236146 Reorder the terms: 2.833333334 + x = -3.270236146 Solving 2.833333334 + x = -3.270236146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -3.270236146 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -3.270236146 + -2.833333334 x = -3.270236146 + -2.833333334 Combine like terms: -3.270236146 + -2.833333334 = -6.10356948 x = -6.10356948 Simplifying x = -6.10356948Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.436902812, -6.10356948}
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