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Simplifying x = 12x2 + -176x + 484 Reorder the terms: x = 484 + -176x + 12x2 Solving x = 484 + -176x + 12x2 Solving for variable 'x'. Reorder the terms: -484 + x + 176x + -12x2 = 484 + -176x + 12x2 + -484 + 176x + -12x2 Combine like terms: x + 176x = 177x -484 + 177x + -12x2 = 484 + -176x + 12x2 + -484 + 176x + -12x2 Reorder the terms: -484 + 177x + -12x2 = 484 + -484 + -176x + 176x + 12x2 + -12x2 Combine like terms: 484 + -484 = 0 -484 + 177x + -12x2 = 0 + -176x + 176x + 12x2 + -12x2 -484 + 177x + -12x2 = -176x + 176x + 12x2 + -12x2 Combine like terms: -176x + 176x = 0 -484 + 177x + -12x2 = 0 + 12x2 + -12x2 -484 + 177x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -484 + 177x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 40.33333333 + -14.75x + x2 = 0 Move the constant term to the right: Add '-40.33333333' to each side of the equation. 40.33333333 + -14.75x + -40.33333333 + x2 = 0 + -40.33333333 Reorder the terms: 40.33333333 + -40.33333333 + -14.75x + x2 = 0 + -40.33333333 Combine like terms: 40.33333333 + -40.33333333 = 0.00000000 0.00000000 + -14.75x + x2 = 0 + -40.33333333 -14.75x + x2 = 0 + -40.33333333 Combine like terms: 0 + -40.33333333 = -40.33333333 -14.75x + x2 = -40.33333333 The x term is -14.75x. Take half its coefficient (-7.375). Square it (54.390625) and add it to both sides. Add '54.390625' to each side of the equation. -14.75x + 54.390625 + x2 = -40.33333333 + 54.390625 Reorder the terms: 54.390625 + -14.75x + x2 = -40.33333333 + 54.390625 Combine like terms: -40.33333333 + 54.390625 = 14.05729167 54.390625 + -14.75x + x2 = 14.05729167 Factor a perfect square on the left side: (x + -7.375)(x + -7.375) = 14.05729167 Calculate the square root of the right side: 3.749305492 Break this problem into two subproblems by setting (x + -7.375) equal to 3.749305492 and -3.749305492.Subproblem 1
x + -7.375 = 3.749305492 Simplifying x + -7.375 = 3.749305492 Reorder the terms: -7.375 + x = 3.749305492 Solving -7.375 + x = 3.749305492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.375' to each side of the equation. -7.375 + 7.375 + x = 3.749305492 + 7.375 Combine like terms: -7.375 + 7.375 = 0.000 0.000 + x = 3.749305492 + 7.375 x = 3.749305492 + 7.375 Combine like terms: 3.749305492 + 7.375 = 11.124305492 x = 11.124305492 Simplifying x = 11.124305492Subproblem 2
x + -7.375 = -3.749305492 Simplifying x + -7.375 = -3.749305492 Reorder the terms: -7.375 + x = -3.749305492 Solving -7.375 + x = -3.749305492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.375' to each side of the equation. -7.375 + 7.375 + x = -3.749305492 + 7.375 Combine like terms: -7.375 + 7.375 = 0.000 0.000 + x = -3.749305492 + 7.375 x = -3.749305492 + 7.375 Combine like terms: -3.749305492 + 7.375 = 3.625694508 x = 3.625694508 Simplifying x = 3.625694508Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.124305492, 3.625694508}
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