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Simplifying x = 2x2 + 18x + 28 Reorder the terms: x = 28 + 18x + 2x2 Solving x = 28 + 18x + 2x2 Solving for variable 'x'. Reorder the terms: -28 + x + -18x + -2x2 = 28 + 18x + 2x2 + -28 + -18x + -2x2 Combine like terms: x + -18x = -17x -28 + -17x + -2x2 = 28 + 18x + 2x2 + -28 + -18x + -2x2 Reorder the terms: -28 + -17x + -2x2 = 28 + -28 + 18x + -18x + 2x2 + -2x2 Combine like terms: 28 + -28 = 0 -28 + -17x + -2x2 = 0 + 18x + -18x + 2x2 + -2x2 -28 + -17x + -2x2 = 18x + -18x + 2x2 + -2x2 Combine like terms: 18x + -18x = 0 -28 + -17x + -2x2 = 0 + 2x2 + -2x2 -28 + -17x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -28 + -17x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(28 + 17x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(28 + 17x + 2x2)' equal to zero and attempt to solve: Simplifying 28 + 17x + 2x2 = 0 Solving 28 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14 + 8.5x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 8.5x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 8.5x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 8.5x + x2 = 0 + -14 8.5x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 8.5x + x2 = -14 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -14 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -14 + 18.0625 Combine like terms: -14 + 18.0625 = 4.0625 18.0625 + 8.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + 4.25) equal to 2.015564437 and -2.015564437.Subproblem 1
x + 4.25 = 2.015564437 Simplifying x + 4.25 = 2.015564437 Reorder the terms: 4.25 + x = 2.015564437 Solving 4.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 2.015564437 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 2.015564437 + -4.25 x = 2.015564437 + -4.25 Combine like terms: 2.015564437 + -4.25 = -2.234435563 x = -2.234435563 Simplifying x = -2.234435563Subproblem 2
x + 4.25 = -2.015564437 Simplifying x + 4.25 = -2.015564437 Reorder the terms: 4.25 + x = -2.015564437 Solving 4.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -2.015564437 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -2.015564437 + -4.25 x = -2.015564437 + -4.25 Combine like terms: -2.015564437 + -4.25 = -6.265564437 x = -6.265564437 Simplifying x = -6.265564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.234435563, -6.265564437}Solution
x = {-2.234435563, -6.265564437}
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