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Simplifying 7.75(x) + -1(-3x2 + 425x + 22675) = 0 Reorder the terms: 7.75x + -1(22675 + 425x + -3x2) = 0 7.75x + (22675 * -1 + 425x * -1 + -3x2 * -1) = 0 7.75x + (-22675 + -425x + 3x2) = 0 Reorder the terms: -22675 + 7.75x + -425x + 3x2 = 0 Combine like terms: 7.75x + -425x = -417.25x -22675 + -417.25x + 3x2 = 0 Solving -22675 + -417.25x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7558.333333 + -139.0833333x + x2 = 0 Move the constant term to the right: Add '7558.333333' to each side of the equation. -7558.333333 + -139.0833333x + 7558.333333 + x2 = 0 + 7558.333333 Reorder the terms: -7558.333333 + 7558.333333 + -139.0833333x + x2 = 0 + 7558.333333 Combine like terms: -7558.333333 + 7558.333333 = 0.000000 0.000000 + -139.0833333x + x2 = 0 + 7558.333333 -139.0833333x + x2 = 0 + 7558.333333 Combine like terms: 0 + 7558.333333 = 7558.333333 -139.0833333x + x2 = 7558.333333 The x term is -139.0833333x. Take half its coefficient (-69.54166665). Square it (4836.043400) and add it to both sides. Add '4836.043400' to each side of the equation. -139.0833333x + 4836.043400 + x2 = 7558.333333 + 4836.043400 Reorder the terms: 4836.043400 + -139.0833333x + x2 = 7558.333333 + 4836.043400 Combine like terms: 7558.333333 + 4836.043400 = 12394.376733 4836.043400 + -139.0833333x + x2 = 12394.376733 Factor a perfect square on the left side: (x + -69.54166665)(x + -69.54166665) = 12394.376733 Calculate the square root of the right side: 111.330035179 Break this problem into two subproblems by setting (x + -69.54166665) equal to 111.330035179 and -111.330035179.Subproblem 1
x + -69.54166665 = 111.330035179 Simplifying x + -69.54166665 = 111.330035179 Reorder the terms: -69.54166665 + x = 111.330035179 Solving -69.54166665 + x = 111.330035179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '69.54166665' to each side of the equation. -69.54166665 + 69.54166665 + x = 111.330035179 + 69.54166665 Combine like terms: -69.54166665 + 69.54166665 = 0.00000000 0.00000000 + x = 111.330035179 + 69.54166665 x = 111.330035179 + 69.54166665 Combine like terms: 111.330035179 + 69.54166665 = 180.871701829 x = 180.871701829 Simplifying x = 180.871701829Subproblem 2
x + -69.54166665 = -111.330035179 Simplifying x + -69.54166665 = -111.330035179 Reorder the terms: -69.54166665 + x = -111.330035179 Solving -69.54166665 + x = -111.330035179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '69.54166665' to each side of the equation. -69.54166665 + 69.54166665 + x = -111.330035179 + 69.54166665 Combine like terms: -69.54166665 + 69.54166665 = 0.00000000 0.00000000 + x = -111.330035179 + 69.54166665 x = -111.330035179 + 69.54166665 Combine like terms: -111.330035179 + 69.54166665 = -41.788368529 x = -41.788368529 Simplifying x = -41.788368529Solution
The solution to the problem is based on the solutions from the subproblems. x = {180.871701829, -41.788368529}
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