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Simplifying 3x2 = 17x + 64 Reorder the terms: 3x2 = 64 + 17x Solving 3x2 = 64 + 17x Solving for variable 'x'. Reorder the terms: -64 + -17x + 3x2 = 64 + 17x + -64 + -17x Reorder the terms: -64 + -17x + 3x2 = 64 + -64 + 17x + -17x Combine like terms: 64 + -64 = 0 -64 + -17x + 3x2 = 0 + 17x + -17x -64 + -17x + 3x2 = 17x + -17x Combine like terms: 17x + -17x = 0 -64 + -17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21.33333333 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + -5.666666667x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + -5.666666667x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + -5.666666667x + x2 = 0 + 21.33333333 -5.666666667x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 -5.666666667x + x2 = 21.33333333 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 = 21.33333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 21.33333333 + 8.027777782 Combine like terms: 21.33333333 + 8.027777782 = 29.361111112 8.027777782 + -5.666666667x + x2 = 29.361111112 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 29.361111112 Calculate the square root of the right side: 5.418589402 Break this problem into two subproblems by setting (x + -2.833333334) equal to 5.418589402 and -5.418589402.Subproblem 1
x + -2.833333334 = 5.418589402 Simplifying x + -2.833333334 = 5.418589402 Reorder the terms: -2.833333334 + x = 5.418589402 Solving -2.833333334 + x = 5.418589402 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 = 5.418589402 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 5.418589402 + 2.833333334 x = 5.418589402 + 2.833333334 Combine like terms: 5.418589402 + 2.833333334 = 8.251922736 x = 8.251922736 Simplifying x = 8.251922736Subproblem 2
x + -2.833333334 = -5.418589402 Simplifying x + -2.833333334 = -5.418589402 Reorder the terms: -2.833333334 + x = -5.418589402 Solving -2.833333334 + x = -5.418589402 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 = -5.418589402 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -5.418589402 + 2.833333334 x = -5.418589402 + 2.833333334 Combine like terms: -5.418589402 + 2.833333334 = -2.585256068 x = -2.585256068 Simplifying x = -2.585256068Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.251922736, -2.585256068}
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