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Simplifying 6x2 + 12x + -97 = 0 Reorder the terms: -97 + 12x + 6x2 = 0 Solving -97 + 12x + 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'. -16.16666667 + 2x + x2 = 0 Move the constant term to the right: Add '16.16666667' to each side of the equation. -16.16666667 + 2x + 16.16666667 + x2 = 0 + 16.16666667 Reorder the terms: -16.16666667 + 16.16666667 + 2x + x2 = 0 + 16.16666667 Combine like terms: -16.16666667 + 16.16666667 = 0.00000000 0.00000000 + 2x + x2 = 0 + 16.16666667 2x + x2 = 0 + 16.16666667 Combine like terms: 0 + 16.16666667 = 16.16666667 2x + x2 = 16.16666667 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 16.16666667 + 1 Reorder the terms: 1 + 2x + x2 = 16.16666667 + 1 Combine like terms: 16.16666667 + 1 = 17.16666667 1 + 2x + x2 = 17.16666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 17.16666667 Calculate the square root of the right side: 4.143267632 Break this problem into two subproblems by setting (x + 1) equal to 4.143267632 and -4.143267632.Subproblem 1
x + 1 = 4.143267632 Simplifying x + 1 = 4.143267632 Reorder the terms: 1 + x = 4.143267632 Solving 1 + x = 4.143267632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.143267632 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.143267632 + -1 x = 4.143267632 + -1 Combine like terms: 4.143267632 + -1 = 3.143267632 x = 3.143267632 Simplifying x = 3.143267632Subproblem 2
x + 1 = -4.143267632 Simplifying x + 1 = -4.143267632 Reorder the terms: 1 + x = -4.143267632 Solving 1 + x = -4.143267632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.143267632 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.143267632 + -1 x = -4.143267632 + -1 Combine like terms: -4.143267632 + -1 = -5.143267632 x = -5.143267632 Simplifying x = -5.143267632Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.143267632, -5.143267632}
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