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Simplifying 5x + 39 + -5 = (3x + -12)(3x + -12) Reorder the terms: 39 + -5 + 5x = (3x + -12)(3x + -12) Combine like terms: 39 + -5 = 34 34 + 5x = (3x + -12)(3x + -12) Reorder the terms: 34 + 5x = (-12 + 3x)(3x + -12) Reorder the terms: 34 + 5x = (-12 + 3x)(-12 + 3x) Multiply (-12 + 3x) * (-12 + 3x) 34 + 5x = (-12(-12 + 3x) + 3x * (-12 + 3x)) 34 + 5x = ((-12 * -12 + 3x * -12) + 3x * (-12 + 3x)) 34 + 5x = ((144 + -36x) + 3x * (-12 + 3x)) 34 + 5x = (144 + -36x + (-12 * 3x + 3x * 3x)) 34 + 5x = (144 + -36x + (-36x + 9x2)) Combine like terms: -36x + -36x = -72x 34 + 5x = (144 + -72x + 9x2) Solving 34 + 5x = 144 + -72x + 9x2 Solving for variable 'x'. Reorder the terms: 34 + -144 + 5x + 72x + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Combine like terms: 34 + -144 = -110 -110 + 5x + 72x + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Combine like terms: 5x + 72x = 77x -110 + 77x + -9x2 = 144 + -72x + 9x2 + -144 + 72x + -9x2 Reorder the terms: -110 + 77x + -9x2 = 144 + -144 + -72x + 72x + 9x2 + -9x2 Combine like terms: 144 + -144 = 0 -110 + 77x + -9x2 = 0 + -72x + 72x + 9x2 + -9x2 -110 + 77x + -9x2 = -72x + 72x + 9x2 + -9x2 Combine like terms: -72x + 72x = 0 -110 + 77x + -9x2 = 0 + 9x2 + -9x2 -110 + 77x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -110 + 77x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 12.22222222 + -8.555555556x + x2 = 0 Move the constant term to the right: Add '-12.22222222' to each side of the equation. 12.22222222 + -8.555555556x + -12.22222222 + x2 = 0 + -12.22222222 Reorder the terms: 12.22222222 + -12.22222222 + -8.555555556x + x2 = 0 + -12.22222222 Combine like terms: 12.22222222 + -12.22222222 = 0.00000000 0.00000000 + -8.555555556x + x2 = 0 + -12.22222222 -8.555555556x + x2 = 0 + -12.22222222 Combine like terms: 0 + -12.22222222 = -12.22222222 -8.555555556x + x2 = -12.22222222 The x term is -8.555555556x. Take half its coefficient (-4.277777778). Square it (18.29938272) and add it to both sides. Add '18.29938272' to each side of the equation. -8.555555556x + 18.29938272 + x2 = -12.22222222 + 18.29938272 Reorder the terms: 18.29938272 + -8.555555556x + x2 = -12.22222222 + 18.29938272 Combine like terms: -12.22222222 + 18.29938272 = 6.0771605 18.29938272 + -8.555555556x + x2 = 6.0771605 Factor a perfect square on the left side: (x + -4.277777778)(x + -4.277777778) = 6.0771605 Calculate the square root of the right side: 2.465189749 Break this problem into two subproblems by setting (x + -4.277777778) equal to 2.465189749 and -2.465189749.Subproblem 1
x + -4.277777778 = 2.465189749 Simplifying x + -4.277777778 = 2.465189749 Reorder the terms: -4.277777778 + x = 2.465189749 Solving -4.277777778 + x = 2.465189749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.277777778' to each side of the equation. -4.277777778 + 4.277777778 + x = 2.465189749 + 4.277777778 Combine like terms: -4.277777778 + 4.277777778 = 0.000000000 0.000000000 + x = 2.465189749 + 4.277777778 x = 2.465189749 + 4.277777778 Combine like terms: 2.465189749 + 4.277777778 = 6.742967527 x = 6.742967527 Simplifying x = 6.742967527Subproblem 2
x + -4.277777778 = -2.465189749 Simplifying x + -4.277777778 = -2.465189749 Reorder the terms: -4.277777778 + x = -2.465189749 Solving -4.277777778 + x = -2.465189749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.277777778' to each side of the equation. -4.277777778 + 4.277777778 + x = -2.465189749 + 4.277777778 Combine like terms: -4.277777778 + 4.277777778 = 0.000000000 0.000000000 + x = -2.465189749 + 4.277777778 x = -2.465189749 + 4.277777778 Combine like terms: -2.465189749 + 4.277777778 = 1.812588029 x = 1.812588029 Simplifying x = 1.812588029Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.742967527, 1.812588029}
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