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Simplifying 2 + 7x + 7x + 49 + -1x2 + 9x + 9x + 81 = 0 Reorder the terms: 2 + 49 + 81 + 7x + 7x + 9x + 9x + -1x2 = 0 Combine like terms: 2 + 49 = 51 51 + 81 + 7x + 7x + 9x + 9x + -1x2 = 0 Combine like terms: 51 + 81 = 132 132 + 7x + 7x + 9x + 9x + -1x2 = 0 Combine like terms: 7x + 7x = 14x 132 + 14x + 9x + 9x + -1x2 = 0 Combine like terms: 14x + 9x = 23x 132 + 23x + 9x + -1x2 = 0 Combine like terms: 23x + 9x = 32x 132 + 32x + -1x2 = 0 Solving 132 + 32x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -132 + -32x + x2 = 0 Move the constant term to the right: Add '132' to each side of the equation. -132 + -32x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + -32x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + -32x + x2 = 0 + 132 -32x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 -32x + x2 = 132 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 132 + 256 Reorder the terms: 256 + -32x + x2 = 132 + 256 Combine like terms: 132 + 256 = 388 256 + -32x + x2 = 388 Factor a perfect square on the left side: (x + -16)(x + -16) = 388 Calculate the square root of the right side: 19.697715604 Break this problem into two subproblems by setting (x + -16) equal to 19.697715604 and -19.697715604.Subproblem 1
x + -16 = 19.697715604 Simplifying x + -16 = 19.697715604 Reorder the terms: -16 + x = 19.697715604 Solving -16 + x = 19.697715604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 19.697715604 + 16 Combine like terms: -16 + 16 = 0 0 + x = 19.697715604 + 16 x = 19.697715604 + 16 Combine like terms: 19.697715604 + 16 = 35.697715604 x = 35.697715604 Simplifying x = 35.697715604Subproblem 2
x + -16 = -19.697715604 Simplifying x + -16 = -19.697715604 Reorder the terms: -16 + x = -19.697715604 Solving -16 + x = -19.697715604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -19.697715604 + 16 Combine like terms: -16 + 16 = 0 0 + x = -19.697715604 + 16 x = -19.697715604 + 16 Combine like terms: -19.697715604 + 16 = -3.697715604 x = -3.697715604 Simplifying x = -3.697715604Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.697715604, -3.697715604}
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