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Simplifying 44(2x * 1x) = 44(3x) + 2 Reorder the terms for easier multiplication: 44(2 * 1x * x) = 44(3x) + 2 Multiply 2 * 1 44(2x * x) = 44(3x) + 2 Multiply x * x 44(2x2) = 44(3x) + 2 Remove parenthesis around (2x2) 44 * 2x2 = 44(3x) + 2 Multiply 44 * 2 88x2 = 44(3x) + 2 Remove parenthesis around (3x) 88x2 = 44 * 3x + 2 Multiply 44 * 3 88x2 = 132x + 2 Reorder the terms: 88x2 = 2 + 132x Solving 88x2 = 2 + 132x Solving for variable 'x'. Reorder the terms: -2 + -132x + 88x2 = 2 + 132x + -2 + -132x Reorder the terms: -2 + -132x + 88x2 = 2 + -2 + 132x + -132x Combine like terms: 2 + -2 = 0 -2 + -132x + 88x2 = 0 + 132x + -132x -2 + -132x + 88x2 = 132x + -132x Combine like terms: 132x + -132x = 0 -2 + -132x + 88x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -66x + 44x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -66x + 44x2)' equal to zero and attempt to solve: Simplifying -1 + -66x + 44x2 = 0 Solving -1 + -66x + 44x2 = 0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.02272727273 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.02272727273' to each side of the equation. -0.02272727273 + -1.5x + 0.02272727273 + x2 = 0 + 0.02272727273 Reorder the terms: -0.02272727273 + 0.02272727273 + -1.5x + x2 = 0 + 0.02272727273 Combine like terms: -0.02272727273 + 0.02272727273 = 0.00000000000 0.00000000000 + -1.5x + x2 = 0 + 0.02272727273 -1.5x + x2 = 0 + 0.02272727273 Combine like terms: 0 + 0.02272727273 = 0.02272727273 -1.5x + x2 = 0.02272727273 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.02272727273 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.02272727273 + 0.5625 Combine like terms: 0.02272727273 + 0.5625 = 0.58522727273 0.5625 + -1.5x + x2 = 0.58522727273 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.58522727273 Calculate the square root of the right side: 0.765001485 Break this problem into two subproblems by setting (x + -0.75) equal to 0.765001485 and -0.765001485.Subproblem 1
x + -0.75 = 0.765001485 Simplifying x + -0.75 = 0.765001485 Reorder the terms: -0.75 + x = 0.765001485 Solving -0.75 + x = 0.765001485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.765001485 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.765001485 + 0.75 x = 0.765001485 + 0.75 Combine like terms: 0.765001485 + 0.75 = 1.515001485 x = 1.515001485 Simplifying x = 1.515001485Subproblem 2
x + -0.75 = -0.765001485 Simplifying x + -0.75 = -0.765001485 Reorder the terms: -0.75 + x = -0.765001485 Solving -0.75 + x = -0.765001485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.765001485 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.765001485 + 0.75 x = -0.765001485 + 0.75 Combine like terms: -0.765001485 + 0.75 = -0.015001485 x = -0.015001485 Simplifying x = -0.015001485Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.515001485, -0.015001485}Solution
x = {1.515001485, -0.015001485}
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