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Simplifying 2x2 + 8x = 1080 Reorder the terms: 8x + 2x2 = 1080 Solving 8x + 2x2 = 1080 Solving for variable 'x'. Reorder the terms: -1080 + 8x + 2x2 = 1080 + -1080 Combine like terms: 1080 + -1080 = 0 -1080 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-540 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-540 + 4x + x2)' equal to zero and attempt to solve: Simplifying -540 + 4x + x2 = 0 Solving -540 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + 4x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + 4x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + 4x + x2 = 0 + 540 4x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 4x + x2 = 540 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 540 + 4 Reorder the terms: 4 + 4x + x2 = 540 + 4 Combine like terms: 540 + 4 = 544 4 + 4x + x2 = 544 Factor a perfect square on the left side: (x + 2)(x + 2) = 544 Calculate the square root of the right side: 23.323807579 Break this problem into two subproblems by setting (x + 2) equal to 23.323807579 and -23.323807579.Subproblem 1
x + 2 = 23.323807579 Simplifying x + 2 = 23.323807579 Reorder the terms: 2 + x = 23.323807579 Solving 2 + x = 23.323807579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 23.323807579 + -2 Combine like terms: 2 + -2 = 0 0 + x = 23.323807579 + -2 x = 23.323807579 + -2 Combine like terms: 23.323807579 + -2 = 21.323807579 x = 21.323807579 Simplifying x = 21.323807579Subproblem 2
x + 2 = -23.323807579 Simplifying x + 2 = -23.323807579 Reorder the terms: 2 + x = -23.323807579 Solving 2 + x = -23.323807579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -23.323807579 + -2 Combine like terms: 2 + -2 = 0 0 + x = -23.323807579 + -2 x = -23.323807579 + -2 Combine like terms: -23.323807579 + -2 = -25.323807579 x = -25.323807579 Simplifying x = -25.323807579Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.323807579, -25.323807579}Solution
x = {21.323807579, -25.323807579}
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