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Simplifying 18 + 44x + 16x2 = 8x2 + 36 Reorder the terms: 18 + 44x + 16x2 = 36 + 8x2 Solving 18 + 44x + 16x2 = 36 + 8x2 Solving for variable 'x'. Reorder the terms: 18 + -36 + 44x + 16x2 + -8x2 = 36 + 8x2 + -36 + -8x2 Combine like terms: 18 + -36 = -18 -18 + 44x + 16x2 + -8x2 = 36 + 8x2 + -36 + -8x2 Combine like terms: 16x2 + -8x2 = 8x2 -18 + 44x + 8x2 = 36 + 8x2 + -36 + -8x2 Reorder the terms: -18 + 44x + 8x2 = 36 + -36 + 8x2 + -8x2 Combine like terms: 36 + -36 = 0 -18 + 44x + 8x2 = 0 + 8x2 + -8x2 -18 + 44x + 8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -18 + 44x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 22x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 22x + 4x2)' equal to zero and attempt to solve: Simplifying -9 + 22x + 4x2 = 0 Solving -9 + 22x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 5.5x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 5.5x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 5.5x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 5.5x + x2 = 0 + 2.25 5.5x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 5.5x + x2 = 2.25 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 2.25 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 2.25 + 7.5625 Combine like terms: 2.25 + 7.5625 = 9.8125 7.5625 + 5.5x + x2 = 9.8125 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 9.8125 Calculate the square root of the right side: 3.132491022 Break this problem into two subproblems by setting (x + 2.75) equal to 3.132491022 and -3.132491022.Subproblem 1
x + 2.75 = 3.132491022 Simplifying x + 2.75 = 3.132491022 Reorder the terms: 2.75 + x = 3.132491022 Solving 2.75 + x = 3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.132491022 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.132491022 + -2.75 x = 3.132491022 + -2.75 Combine like terms: 3.132491022 + -2.75 = 0.382491022 x = 0.382491022 Simplifying x = 0.382491022Subproblem 2
x + 2.75 = -3.132491022 Simplifying x + 2.75 = -3.132491022 Reorder the terms: 2.75 + x = -3.132491022 Solving 2.75 + x = -3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.132491022 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.132491022 + -2.75 x = -3.132491022 + -2.75 Combine like terms: -3.132491022 + -2.75 = -5.882491022 x = -5.882491022 Simplifying x = -5.882491022Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.382491022, -5.882491022}Solution
x = {0.382491022, -5.882491022}
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